Seminars (BSM)

We show how extensions of conventional differential geometry, so called "generalised geometry", give a natural way of formulating type II and eleven-dimensional supergravity theories, unifying the bosonic fields and symmetries. There is a natural action of the U- and T-duality groups E_d(d) and O(d,d) and the formalism shows that the supergravity theories have an enhanced local symmetry. By introducing the analogue of the Levi-Civita connection we find that the action and equations of motion simplify, writable in terms of a generalised Ricci tensor. The connection also encodes the supersymmetry variations and fermionic equations of motion. There are interesting implications for describing supersymmetric backgrounds and connections to the embedding tensor formalism.

We will discuss reductions of M-theory and type II theories to four dimensions preserving N=1 and N=2 supersymmetry, in the language of exceptional generalized geometry. We will introduce the relevant structures which encode the NSNS and RR degrees of freedom, discuss the geometry of their orbits under the action of the U-duality group (i.e., the moduli space metrics), and how they enter in the superpotential.

I will describe the relation of the C-field to String structures, which are essentially Spin structures on loop space, and explain how these structures capture certain geometric and topological aspects of M-branes.

Lagrangian cycles will be constructed for algebraic knots in the context of large N duality via conifold transitions. It will be explained how this construction yields a physics derivation of a conjecture of Oblomkov and Shende on HOMFLY polynomials and plane curve singularities. This is joint work with V. Shende and C. Vafa.

I will explain how the wall-crossing behaviour of D-brane instantons in type II Calabi-Yau compactifications is captured by a certain hyperholomorphic line bundle over a hyperkähler manifold. This construction relies on a general duality between 4n-dimensional quaternion-Kähler and hyperkähler spaces with certain continuous isometries. The continuity of the moduli space metric across walls of marginal stability is encoded in non-trivial identities for the Rogers dilogarithm, which are shown to be a consequence of the motivic Kontsevich-Soibelman wall-crossing formula. Finally, I will offer some speculations on how the construction is modified in the presence of NS5-brane effects.

We study pure Seiberg-Witten theories with SU(r+1) and Sp(2r) gauge groups with no flavors. We study singularity loci of moduli space of the Seiberg-Witten curve. Using exterior derivative and discriminant operators, we can find Argyres-Douglas loci of the SW theory. We also compute BPS charges of the massless dyons of SU and Sp SW theory. In a detailed example of C_2=Sp(4), we find 6 points in the moduli space where we have 2 massless BPS dyons, and 3 of them give Argyres-Douglas loci. We show that BPS charges of the massless dyons jump as we go across Argyres-Douglas loci, giving an explicit example of Argyres-Douglas loci living inside the wall of marginal stability.

I will discuss connections between sporadic groups and modular forms including the original connection between the monster and the modular function J, the more recent connections between the Mathieu group M24 and the mock modular form appearing in the decomposition of the elliptic genus of K3 surfaces into N=4 characters, and some work in progress which generalizes this latter connection to other groups and Jacobi forms.

We investigate Chern-Simons theories coupling to vector matter. These kinds of models are quite interesting in the following sense. Firstly, they provide us with infinitely many interacting conformal field theories (CFT) with Lagrangian description, which enables us to study CFT in a direct calculation. Secondly, they are likely to be dual to higher spin theories in AdS4 beyond the conjecture by Klebanov-Polyakov. After a belief introduction of this background, I will talk about U(N) Chern-Simons theories coupling to vector-like (fundamental/anti-fundamental) matter(boson or fermion). It turns out that these kinds of models can be exactly solved in the 't Hooft limit by employing a standard large N technique. I will explain the details on this when the matter includes pure fermion or boson. If time permits, I will talk about the case including both in a supersymmetric way, which is work in progress.

We study an index which counts BPS bound states of instanton particles in 5d maximal SYM, and use it to explore the 6d (2,0) SCFT for M5-branes compactified on a circle in its Coulomb and symmetric phases.

I'll give an overview of automorphic forms beyond SL(2), explaining some of the highlights of the theory and several of its fundamental unresolved challenges. I will keep to the analytic side, emphasizing the impact of the Langlands' program and also some results which have been useful in string theory.

Spinorial geometry techniques can be used to classify the near-horizon geometries of supersymmetric black holes in String/M-theory. I will illustrate this by presenting the classification of near horizon geometries in IIB supergravity coupled to a non-zero self-dual 5-form. The resulting geometries are generically described by a restricted Calabi-Yau with (hidden) torsion structure. Examples of such solutions will be considered, including a large class of AdS solutions.

Despite AdS5 S5 being self-dual under a combination of bosonic and fermionic T-dualities, the same has yet to be said for AdS4 CP3. However, evidence from D=3 scattering amplitude calculations hint strongly at some self-duality. We explain the obstacles in the context of pp-waves and the D1-D5 near-horizon and comment on whether beta-deformed SYM inherits the same symmetries.

We summarize our recently proposed correspondence between 3d N=2 gauge theories and 3d manifolds. If time permits, we also comment on connections with cluster algebras and dimer models.

Maximally supersymmetric string theory compactified on d-dimensional torus is invariant under the non-perturbative U-duality groups E_{d+1}(Z). We will present the construction of the automorphic functions relevant for the supersymmetric protected BPS interactions in the low-energy expansion of maximal supersymmetric effective action in various dimensions. We will show that the support of the non-vanishing Fourier coefficients for these automorphic form is given by the expected BPS conditions one can derive from the supersymmetric conditions.

I will show how loop space can be used in the description of M5-branes. I will focus mainly on the description of self-dual strings as well as a self-dual string analogue of magnetic bags. I will develop a Nahm transform for both cases and construct a number of explicit solutions. I will also show how loop space gives a natural interpretation to a recently proposed set of N=(2,0) supersymmetric equations which might describe M5-branes.

The six-dimensional (2,0) M5-brane CFT was recently conjectured to be obtainable as the strong-coupling limit of five-dimensional, maximally supersymmetric Yang-Mills theory. In this talk we will first review the arguments leading to this claim. We will then present new evidence in its favour through the study of the M2/M5 bound state, which provides an M-theoretic realisation of the Myers brane-polarisation effect.

We review how the counting of BPS states of D-branes in Type IIA string theory can be captured by enumerating the instanton solutions in a six-dimensional noncommutative N=2 gauge theory; mathematically, the instanton contributions are related to Gromov-Witten and Donaldson-Thomas curve counting invariants, which in this context have natural higher-rank generalisations in the Coulomb branch of the gauge theory. We discuss some of the integrability properties of the resulting partition functions, including a novel reformulation as an infinite rank unitary matrix model. We define a stacky version of the gauge theory whose instanton solutions compute noncommutative Donaldson-Thomas invariants for abelian orbifold singularities. We also discuss how N=4 supersymmetric Yang-Mills theory in four dimensions is analogously related to curve counting on toric surfaces

We construct a non-Abelian gauge theory of chiral 2-forms (self-dual gauge fields) in 6 dimensions with a spatial direction compactified on a circle of radius R. It has the following two properties. (1) It reduces to the Yang-Mills theory in 5 dimensions for small R. (2) It is equivalent to the Lorentz-invariant theory of Abelian chiral 2-forms when the gauge group is Abelian. Previous no-go theorems prohibiting non-Abelian deformations of the chiral 2-form gauge theory are circumvented by introducing nonlocality along the compactified dimension.

Starting from double field theory I explain a natural geometric framework in order to describe the so-called non-geometric Q and R fluxes.

When approaching a spacelike singularity the BKL conjecture states that the classical relativity dynamics are governed by chaotic oscillations. These can be alternatively described using a so-called cosmological billiard. When quantising this system one is led to automorphic forms of hyperbolic Weyl groups. The construction of some of these automorphic forms can be phrased conveniently using division algebras. If time permits some features of other Eisenstein series will also be discussed.

String theory is at the cutting edge of theoretical physics. Its deep goal is to unify the conflicting paradigms of quantum mechanics and relativity. In doing so, string theory brings up new ways of seeing the world, with hidden dimensions and novel surprising symmetries and relationships. This event will begin with an accessible introduction to string theory by David Berman followed by a presentation and discussion with Grenville Davey on his art and how aspects of string theory and contemporary physics have been an inspiration. A wine reception will follow.

We review the construction of supergravity solutions in six dimensional supergravity which are preserve half the super symmetries of the AdS3 x S3 vacuum and give a realization of 2 dimensional interface CFTs of the Janus type. By relaxing the regularity conditions we enlarge the space of solutions to include two new half-BPS configurations, which we refer to as the cap and funnel. We present evidence that solutions which include caps can be used to give a holographic realization of boundary CFTs.

We first review the general features underlying the construction of the 3D New Massive Gravity theory. Next, we show in which sense, at least at the linearized level, this theory can be extended to higher dimensions. An important role is played by exotic representations of massive spin 2. The prospect for interactions is discussed

I shall talk about a class eight derivative interactions in the effective action of type IIB string theory compactified on T^2. These 1/2 BPS interactions have moduli dependent couplings. I shall impose the constraints of supersymmetry to show that each of these couplings satisfy a first order differential equation on moduli space which relate it to other couplings in the same supermuliplet. The couplings which only depend on the SO(2)\SL(2,R) moduli satisfy Laplace equation on moduli space. On the other hand, the ones which only depend on the SO(3)\SL(3,R) moduli are far more complicated, and satisfy Poisson equation on moduli space, where the source terms are given by other couplings in the same supermultiplet.

This talk includes some general remarks about formulating supergravity theories on manifolds with boundary, and addresses the specific problem of moduli stabilisation with a vanishing cosmological constant in Heterotic M theory.

I will talk about a recent construction for an action for non-abelian 2-form in 6-dimensions. The action consists of a non-abelian generalization of the abelian action of Perry and Schwarz for a single M5-brane. It admits a self-duality equation on the field strength as the equation of motion. It has a modified 6d Lorentz symmetry. On dimensional reduction on a circle, our action gives the standard 5d Yang-Mills action. Based on these properties, we propose that our theory describes a theory of multiple M5-branes in flat space.

Only a few years old, the idea that kinematic building blocks of scattering amplitudes have the same structure and properties as the Lie-algebra color factors - known as color-kinematics duality - has proven quite fruitful. Although the origins of the kinematic Lie-algebra structure remains unknown, it has improved our understanding of non-planar gauge theory and gravity. In this talk, I will review the status of color-kinematics duality at tree and loop level, illuminating the open problems as well as the techniques for calculating non-planar Yang-Mills and gravity loop amplitudes.

I will describe the application of a bootstrap program for scattering amplitudes based on analytic constraints from the operator product expansion for light-like Wilson loops and multi-Regge limits. Together with an ansatz for the space of relevant functions these place powerful constraints on the form of multi-loop amplitudes.

We discuss the string junctions in the Coulomb phase of 6 dimensional superconformal (2,0) theories as candidates for the N^3 degrees of freedom of the fundamental theory.

Joint conference day organised with DAMTP, University of Cambridge

Joint conference day organised with DAMTP, University of Cambridge

Joint conference day organised with DAMTP, University of Cambridge

Joint conference day organised with DAMTP, University of Cambridge

We have recently calculated the superconformal index on 5d N=1 supersymmetric theory with SU(2) gauge group and N fundamental hypermultiplets in the conformal limit where the gauge coupling goes to infinite. This index shows as expected that the global symmetry in the conformal limit is enhanced from the flavor SO(2N) symmetry and the global U(1) symmetry for the instanton number to the exceptional group E(N+1).

I will discuss correlation functions in the worldline of an observer in the static patch of dS space. I will show how an emergent conformal structure appears that points towards a holographic dual in terms of a conformal quantum mechanics. Furthermore I'll make contact with the better studied dS/CFT picture by analyzing the spectrum of quasi-normal modes.

The AdS/CFT correspondence of string theory offers the hope of direct, mathematically precise and systematically correctable study of strongly coupled quantum systems. Progress toward this goal will be described in the context of a simple example: the probe D-brane dual of a class of relativistic field theories which resemble the description of graphene by relativistic fermions. A hypothesis that graphene can be such a strongly correlated quantum fluid and at the same time exhibit behaviours which are well modeled by non-interacting relativistic fermions will be discussed as well as some interesting new phases of matter which are suggested by the D-brane construction.

I will review some recent work on complex, glassy systems in string theory and cosmology.

I'll discuss the quantum geometry of elliptically fibered Calabi-Yau threefolds. A holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base. T-duality on the fibre implies that the topological string free energy also captures the BPS-invariants of D4-branes wrapping the elliptic fibre and a class in the base. We verify this proposal by explicit computation of the BPS invariants of 3 D4-branes on the rational elliptic surface.

Schroedinger spacetimes geometrically realize the nonrelativistic conformal group, reason for which they have been proposed as holographic duals to strongly coupled non-relativistic CFTs. On the other hand, it has been recently shown that black holes in three-dimensional Schroedinger spacetimes exhibit a previously unknown Virasoro asymptotic symmetry, which is indicative of a full conformal symmetry. To uncover it, I will construct a Fefferman-Graham-like expansion for the relevant modes in asymptotically three-dimensional Schroedinger spacetimes by mapping them to an auxiliary AdS(3) spacetime, and show that the renormalized on-shell action for these modes is identical to the one for the gravity modes in the auxiliary AdS(3). The holographic stress-energy tensor one obtains by this procedure is symmetric, conserved and its trace yields the same conformal anomaly as in AdS(3).

In this talk we will revisit the computation of greybody factors using a novel set of tools based on the monodromy technique. Our aim is to emphasize that the analytic properties of the black hole background play a crucial role in the scattering problem. In particular, acknowledging the existence of the inner horizon allows for exact expressions of the transmission and reflection coefficients without taking any low or high frequency approximation. More interestingly, this approach sheds light on the CFT interpretation of the B-H entropy as a Cardy formula for a large class of black holes in 4D and 5D.

Lifshitz space-times with critical exponent z=2 can obtained by dimensional reduction of Schroedinger space-times with critical exponent z=0. The latter space-times are asymptotically AdS solutions of AdS gravity coupled to an axion-dilaton system (or even just a massless scalar field). This basic observation is used to perform holographic renormalization for 4-dimensional asymptotically locally Lifshitz space-times by dimensional reduction of the corresponding problem of holographic renormalization for 5-dimensional asymptotically AdS space-times coupled to an axion-dilaton system. In this setup the 4-dimensional structure of the Lifshitz Fefferman-Graham expansion and the structure of the counterterm action, including the scale anomaly, will be discussed.

In recent years the conformal bootstrap has emerged as a surprisingly powerful tool to study CFTs in dimensions greater than two. In this talk I will explain how crossing symmetry of the four-point function of scalar operators can be used to extract very non-trivial constraints on the spectrum of a putative CFT in arbitrary spacetime dimension. Applying these techniques in D=3 we will find that the 3D Ising model lies at a special point in the space of CFTs. Moreover, we will show that constraints from conformal invariance can be used to significantly reduce the error in the known estimates for the dimensions of operators and suggest a method to generalize this to a compute the dimensions of all operators in the theory. Time permitting, I will mention some more general applications of this technology, including holography.

We study scattering amplitudes of higher spin closed-string states off D-brane bound-states. For states in the first Regge trajectory we find remarkable simplifications both at tree level and at one loop. We discuss the high energy behavior in the Regge limit and comment on the validity of the eikonal approximation in this regime.

We review the fake superpotential formalism for describing extremal black holes and discuss its possible extensions to the case of black holes in asymptotically AdS spacetimes.

Working in N=4 gauged supergravity, we analyze the conditions for five-dimensional supersymmetric domain walls, which correspond to holographic RG flows. Applying our results to a class of consistent truncations of string theory, we obtain a general flow for SCFT deformations, as well as a new flow closely related to the resolved conifold. We also discuss a superpotential for the baryonic branch of the Klebanov-Strassler solution.

The possible relation between the effective action for N=2 supergravity with couplings proportional to the square of the Weyl tensor and the topological string partition function is explored. A number of systematic features is extracted with particular attention to the presence of non-holomorphic corrections.

The boundary conditions of general black holes in asymptotically flat spacetimes can be modified such that a conformal symmetry emerges. The black holes with asymptotic geometry modified in this manner satisfy the equations of motion of minimal supergravity in one dimension more. Their symmetry suggests that a dual conformal field theory description exists that can account for the black hole entropy even in the case of black holes that are far from extremality.

I will review the general construction of non-extremal black-hole and black-brane solutions of N=2,d=4 and d=5 supergravity coupled to vector multiplets, and their properties. I will describe the explicit solutions of a few models, their extremal (supersymmetric and non-supersymmetric) limits, entropies, non-extremality functions etc. and a formalism that simplifies dramatically the search and construction of those solutions.

Recently, we showed by explicit computations that the product of all the horizon areas is independent of the mass, regardless of the topology of the horizons. The universal character of this relation holds for all known five dimensional asymptotically flat black rings, and for black strings. This gives further evidence for the crucial role that the thermodynamic properties at each horizon play in understanding the entropy at the microscopic level. To this end we proposed a 'first law' for the inner Cauchy horizons of black holes. The validity of this formula, which seems to be universal, was explicitly checked in all cases.

We study how the hydrodynamics of a black brane changes when we enclose it in a finite cylindrical cavity with Dirichlet boundary conditions. For neutral black branes, we see how the Gregory-Laflamme instability switches off and study the critical point where the instability disappears. For black D3 branes, as the cavity radius decreases one obtains the sequence of descriptions "blackfolds > fluid/AdS-gravity > membrane paradigm". We show that, to leading order above extremality, "sound comes from the throat".

A unitary resolution of the black hole information problem, or unitarity crisis, appears to require transfer of quantum information from black holes to their surroundings, in conflict with field-theory locality. One can both model and constrain such evolution. A possible general setting for such evolution, capturing some aspects of locality, is in a Hilbert-space network.

I will discuss results from arXiv:1112.5156 on string one-loop contributions to the Kahler metric of D-brane moduli (positions and Wilson lines), in toroidal orientifolds with branes at angles, and minimal supersymmetry. Also I will outline some more recent results on similar calculations for closed string moduli.

We shall detail points of interest for string model builders coming from recent data, providing some targets that model builders may like to hit. In particular, we shall discuss higgs and supersymmetry searches, and infer some general statements about the spectra and naturalness of models. We shall also mention the t tbar asymmetry from the Tevatron, which disagrees with Standard Model expectations, recent relevant B decay results, Daya bay implications for neutrino masses and mixings and an inferred 130 GeV line in gamma rays coming from our galaxy.

I will present recent results which try to combine moduli stabilisation and chiral model building both in the geometric regime and at the quiver locus within a fully consistent type IIB string compactification described in terms of toric geometry. I will also briefly discuss some cosmological applications and a new way to get dS vacuua in a manifestly supersymmetric effective action.

Weakly interacting slim particles (WISPs) appear often in extensions of the standard model, string theory in particular. This is the case of pseudo Nambu Goldstone Bosons, stringy axions, moduli, hidden photons, mini-charged particles and a long etc. The strongest bounds on their existence come frequently from cosmology and astrophysics but, in particular cases, laboratory experiments at the low energy, high intensity frontier, are more relevant. In this talk we review the most relevant astro/cosmo arguments and laboratory experiments used to constrain the existence of WISPs, focusing on the most discussed cases of axion-like particles (ALPs) and Hidden Photons. We will also pay attention to the recent anomalies which could be pointing to the existence of WISPs: the anomalous cooling rate of white dwarfs and the transparency of the Universe to gamma-rays. Finally, we will conclude discussing WISPs as testable cold dark matter candidates.

We consider closed bosonic string theory with flat background and constant H-flux. Up to linear order in the flux, this is a solution to the string equations of motion and we are able to define a world-sheet conformal field theory framework to compute scattering amplitudes. In the easiest cases of n-point tachyon amplitudes, we use the properties of the Rogers dilogarithm function to speculate about the nature of the product of functions on spacetimes T-dual to the original configuration.

After reviewing some virtues and problems of the minimal supersymmetric standard model (MSSM), I will show that, if one demands anomaly freedom and fermion masses, only R symmetries can forbid the supersymmetric Higgs mass term mu. I will then prove that R symmetries are not available in conventional grand unified theories (GUTs) and argue that this prevents natural solutions to the doublet-triplet splitting problem in four dimensions. On the other hand, higher-dimensional GUTs do not suffer from this problem. I will briefly discuss an explicit string-derived model in which the mu and dimension five proton decay problems are solved by an order four discrete R symmetry, and comment on the higher-dimensional origin of this symmetry.

We describe an efficient algorithmic test for the Swiss Cheese property in Calabi-Yau threefolds, which is typically considered in the context of moduli stabilization in Large Volume Scenarios of type~IIB flux compactifications of string theory. The algorithm recasts the issue of moduli stabilization at large volume into the language of algebraic geometry, thereby allowing for a large scale computational analysis. Preliminary results of a scan of Calabi-Yau three folds with small Hodge numbers will be presented.

Non-geometric fluxes appear in four-dimensional gauged supergravities through specific terms in the potential. These terms are of phenomenological interest for the matters of moduli stabilization or de Sitter solutions. Unfortunately, their ten-dimensional origin, and their relation to non-geometry, remain unclear. In this talk, I will present recent progress on these questions. Thanks to a field redefinition in ten-dimensional supergravity, one makes the non-geometric Q and R fluxes appear, and additionally restores a standard notion of geometry. A dimensional reduction can then be performed, and the four-dimensional non-geometric terms of the scalar potential are recovered.

It has been shown that non-geometric fluxes appear in ten-dimensional supergravity by performing a field redefinition. Following a similar strategy in double field theory surprisingly allows for a geometric interpretation of these fluxes. More precisely, the Q-flux appears as part of a dual curvature scalar, reminiscent of the geometric flux f. The R-flux turns out to be a tensor and appears in the same way as the usual H-flux does. Solving the strong constraint connects this formalism to the ten-dimensional approach. Furthermore, some recent lifts of four-dimensional gauged supergravity to double field theory can be matched.

I will review some recent work on spontaneous partial supersymmetry breaking in extended supersymmetry. I will first describe the no-go theorems which forbid N=2 to N=1 spontaneous supersymmetry breaking in global and local supersymmetry, before showing how they are circumvented. I will then discuss some new techniques involving the embedding tensor formalism which allow us to study this problem systemically and find the low-energy effective theory in the N=1 vacuum. This leads to interesting insights into spontaneous partial supersymmetry breaking in supergravity and string theory, as well as new results in quaternionic geometry.

Flux compactifications are an important building block for obtaining (semi-)realistic string theory vacua. Conventional H- and geometric flux are rather well-understood in this setting, however, non-geometric fluxes are understood to a far lesser degree.

In this talk, it is first reviewed how certain fluxes can be treated as the torsion of a connection, and how gravity theories can be formulated via the Palatini formalism. Next, this formalism is extended to higher orders in the curvature leading to constraints on the fluxes, which are then interpreted as Bianchi identities.

We undertake a systematic scan of vector bundles over the database of torically generated Calabi-Yau three-folds in the context of heterotic string compactifications. Specifically, we construct positive monad bundles over Calabi-Yau hypersurfaces in toric varieties, with the number of Kahler moduli equal to one, two and three, and extract physically interesting models. We select models which can possibly lead to three families of matter after quotienting by a freely-acting discrete symmetries and including Wilson lines. About 2000 such models on two manifolds are found.

String compactifications incorporating non-vanishing H-flux have received increased attention over the past decade for their potential relevance to the moduli stabilization problem. Their internal spaces are in general not Kähler and, therefore, not Calabi-Yau. In the heterotic string an important technical problem is to construct gauge bundles on such spaces. I will present a method of how to explicitly construct gauge bundles over homogeneous nearly-Kähler manifolds of dimension six. These bundles solve the heterotic string including first order alpha' corrections and allow for non-vanishing flux. I will also discuss some of the arising implications for model building.

Related Links •http://arxiv.org/abs/1107.3573 - presented results are based on this paper

Fluxbrane inflation (arXiv:1104.5016) is a recently proposed stringy realisation of D-term hybrid inflation, featuring some appealing phenomenological characteristics. In contrast to other brane inflation models, fluxbrane inflation has a naturally flat inflaton potential at leading order and thus does not rely on strong warping or an extremely anisotropic compact space. Additionally, the scenario contains a mechanism which allows one to avoid the clash with observational bounds due to cosmic string production rather easily. In my talk, I will present the most interesting aspects of the model and, furthermore, discuss recent progress and new challenges regarding moduli stabilisation (in the context of the LARGE volume scenario) as well as the impact of higher-order corrections on the flatness of the inflaton potential.

Quantum Cosmology tackles the quantum description of the early universe. It is aimed as an accessible primer that covers the basics, critically discussing ideas and concepts that comprise our current knowledge. The scope for analyzing quantum cosmological models within a supersymmetric framework is pointed.

As much as possible, it summarizes what we know, what we think we know and what we think we do not know on an equal footing. It is focused for ‘young’, inquisitive minds eager to embark on in-depth research in this field. It is hoped to suggest the tools researchers will need to go on their own, pushing them to ask the right questions rather than seek definitive answers.

I will discuss how the U(1) vector fields that live on the worldvolumes of D-branes in Type IIB string theory may play the role of vector curvatons and hence give rise to distinctive features in the spectrum and bispectrum of the curvature perturbation. I will first consider vector fields on D3-branes in open-string inflation, as a means of illustrating the principle. I will then discuss a D7-brane vector curvaton scenario in closed-string inflation.

First I discuss anomalies in heterotic compactifications. I argue that anomalies will generically not be universal, and illustrate this point by an explicit example of a heterotic orbifold blowup. Then, I investigate the origin of discrete (R and non-R) symmetries on smooth Calabi-Yau manifolds via an GLSM approach.

Using M/F-theory duality, I will relate the quantization of the G-flux in M-theory to the one of the gauge flux on type IIB D7-branes prescribed by Freed-Witten anomaly cancellation. The correspondence is shown for all unitary and symplectic Kodaira singularities, by explicitly constructing appropriate 4-cycles in the M-theory elliptic fourfold, which are able to detect the global anomaly.

I will discuss the next to leading order corrections to the heterotic bundle constructions of Klaput, Lukas and Matti. I will show how these constructions lead to a non-zero H-flux at next to leading order, and how this flux may be used to stabilise either the dilaton, or the volume of the internal space. I will then add a gaugino condensate to the 4D supergravity, and show that for certain bundle choices it is possible to stabilise all moduli at consistent values.

Anti-branes in the deformed conifold are used for example to construct de Sitter vacua. In the probe approximation, they lead to a metastable state. I will present work done over the last three years to go beyond the probe approximation by taking into account the back-reaction of the anti-branes. To be, or not to be (a metastable state), that is the question. We are pinning down the answer.

We attempt an estimate for the distribution of the tensor mode fraction $r$ over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.

I will discuss various aspects of model building and moduli stabilization in heterotic string theory. This will include building standard models from pure abelian gauge field configurations, and investigating compactifications on manifolds admitting SU(3) structures with intrinsic torsion.

We discuss holographic superconductivity in the context of IIB on AdS_5 x T^{1,1}. In the spectrum on the gravity side, there are several modes with potential instabilities. In addition to the one identifed by Gubser et al, we point out that there is another, potentially more unstable mode. Moreover, we propose a concrete model for the dynamics of this mode. With this proposal at hand, we show that it indeed dominates the thermodynamics at low temperatures.

The notion of non-geometric flux was introduced in string theory to correctly describe the degrees of freedom in four-dimensional effective superpotentials of type II flux compactifications. Whereas the H-flux is simply the field strength of the NS-NS B-field and the f-flux can be interpreted as the structure constants of a non-holonomic basis of the tangent bundle, the physical and mathematical properties of the remaining Q- and R-fluxes are to a great extent unknown. In this talk, we will first use the notion of a (quasi-)Poisson structure to re-derive directly on the tangent bundle the commutation relations containing all four fluxes as structure constants. As a consequence, we get Bianchi-type identities for the fluxes by writing down the Jacobi-identities for the algebra. Using these Bianchi-identities and the theory of quasi Lie-algebroids, we are able to identify the associated Courant algebroid structure, which is essential for dealing with all fluxes being non-zero.

M5-instanton corrections to the superpotential in four-dimensional F-theory compactifications have a moduli-dependent prefactor which contains interesting physical content. In two examples obtained via heterotic duality, I will show that the entire vanishing locus of the prefactor can be understood via simple F-theory physics, often occurring at enhanced symmetry points in the complex structure moduli space. If time permits, I will discuss the relationship between line bundle cohomology on a distinguished curve in the instanton worldvolume and the intermediate Jacobian of the M5-instanton.

Results are reviewed for the first stages of Baylor University’s ongoing systematic statistics investigations of the parameter space of free fermionic heterotic string models. Presented is the complete set of D = 4, 6 models with either maximal or completely broken spacetime SUSY that are constructed from the untwisted sector and exactly one additional gauge sector containing anywhere from order 2 through 32 twists. All additional models generated to date with additional twisted gauge sectors are also discussed. A vast degeneracy among models appears: from the roughly 2 billion D = 4 models with a single twist sector, only 577 physically distinct models appear. 68 of these have N = 4 SUSY and 509 have completely broken SUSY. To date, no new physically distinct models appear among any of those formed from two or more twisted gauge sectors. Several redundancies among D= 4 models and among D= 6 models are proven to result from redundancies already present among D= 10 models . Methods to reduce redundancies in D= 4, 6 systematic searches are summarized. Statistics regarding the appearance of various combinations of gauge group factors and of GUT groups among the set of 577 physically unique models are presented. Lastly, moving briefly to models with matter sectors, a model with an even number D of large space-time dimensions is shown to always have maximal SUSY, if it is formed from the untwisted sector and a sector with a massless left-mover and an odd ordered right-mover.

Moduli stabilization in the Large Volume Scenario requires a specific kind of six-dimensional Calabi-Yau geometry for the compactification procedure, which is being referred to as "Swiss Cheese" due to the presence of certain holes for instanton wrappings. Only a handful of such manifolds are known explicitly. I will give an overview of the Large Volume Scenario and present recent progress on a general scan of the Calabi-Yau threefold landscape for the Swiss Cheese property.

I report on a new class of N=1 dualities relating different gauge theories arising from D3 branes probing orientifold singularities. These dualities provide new, nontrivial solutions to the 't Hooft anomaly matching conditions. I discuss an infinite class of orbifold singularities where the duality can be interpreted as S-duality in ten dimensions. I also discuss non-orbifold singularities, and the microscopic interpretation of the duality in terms of an orientifold transition between compact O7+ and O7- planes.

We discuss the effective theory of F-theory compactifications by using the M-theory dual. Two main results are highlighted: (1) the chiral index of a 4D F-theory compactification can be determined by four-form flux when comparing 3D Chern-Simons theories at one loop, (2) the inclusion of warping effects due to fluxes in M-theory is crucial to determine corrections to the F-theory effective theory even if in the latter warping effects can be neglected.

I will discuss the realization of non-abelian discrete gauge symmetries in field theory and string theory, and present several classes of string models exhibiting non-abelian discrete gauge symmetries. In models of magnetized/intersecting D-branes, the discrete symmetries impose non-trivial constraints on Yukawa couplings, and correspond to interesting flavour symmetries in MSSM-like models.

D-brane worlds have provided a geometrically intuitive approach for Standard Model (SM) engineering within string theory compactifications. While the types and ranks of gauge groups and the chiral matter content are tackled in a straightforward manner, it remains on the one hand an open question if the SM can be obtained on rigid D-branes - without continuous gauge symmetry breaking along flat directions and with non-trivial D-brane instanton contributions to the effective action - and on the other hand if such models are consistent with low-energy data. The T6/Z(2)xZ(6') orbifold with discrete torsion admits a plethora of left-right symmetric `local models' without exotic matter in the adjoint, symmetric or antisymmetric representation. However, `global' completions usually come at the cost of introducing new exotic states in bifundamental representations. It furthermore turns out that USp(2) and SO(2) in place of U(2) symmetries can at most provide one particle generation. Last but not least, it turns out that for any T6/Z(2)xZ(2M) orbifold with discrete torsion and tilted tori, orientifold invariant stacks of D6-branes carry USp(2N) or SO(2N) gauge groups depending on their relative position to the exotic O6-plane. The new classification reduces the number of K-theory constraints. If time permits, I will briefly comment on the drastic change in the pattern of Yukawa couplings on orbifolds compared to the six-torus using a T6/Z6' example. As a result, quark Yukawas can provide large mixings while lepton Yukawas are flavour diagonal at leading order. Also the rule of `one massive generation only' is circumvented.

Non-perturbative effects such as gaugino condensation on a stack of D7-branes are an essential ingredient in several celebrated moduli-stabilisation schemes in type IIB string theory. At the level of the four-dimensional effective theory, the non-perturbative effects induce a non-perturbative superpotential. In particular, new Yukawa interactions can be generated. Type IIB orbifold models contain the essential features to study these non-perturbative corrections to the superpotential in string compactifications. I will describe under which conditions new Yukawa couplings arise in these settings and generalise the results to more realistic string models. Most importantly, I will show that the flavour structure of the induced Yukawa couplings is not aligned with the tree-level flavour structure, thus introducing a new source of flavor violation.

I will discuss the mass spectrum of four-dimensional {\cal N}=1 supergravity in which the Kähler potential and superpotential are taken to be random functions of N chiral superfields. For both supersymmetric and non-supersymmetric critical points, the ensemble of Hessian matrices can be efficiently studied through the ‘Coulomb gas’ formulation of Random Matrix Theory. At large N, the supersymmetric AdS vacua have a very peculiar spectrum which typically includes many BF-allowed tachyons, and I will briefly discuss the prospects of obtaining metastable de Sitter vacua from an ‘uplift’ of a supersymmetric AdS vacuum. An exponentially small fraction de Sitter critical points with spontaneously broken supersymmetry are metastable vacua, and I will discuss how the Coulomb gas formulation can be used to find the joint probability distribution of the masses, the fraction of critical points which are vacua, and the spectrum of the vacua. I will conclude by b riefly discussing some cosmological consequences of these results.

In the last decade, a framework in which string dualities are implemented at the supergravity level has been developed, i.e., the so-called embedding tensor formalism. However, the connection between this formalism and string theory realisations remains still obscure since most of the supergravities obtained by using the embedding tensor formalism correspond to very exotic (non-)geometries in the string side.

In this talk we consider type II flux backgrounds compatible with the absence of brane sources, and construct their explicit embedding into maximal D=4 supergravity. This enables us to investigate the critical points, mass spectra and gauge groups of such "exceptional" backgrounds in a systematic way. We will chart the landscape of vacua in some specific setups which are relevant from the string theory viewpoint and discuss the issues of stability and supersymmetry at those vacuum solutions. Finally we will point towards some natural extensions of the results.

There has been a lot of efforts during the last decade in order to provide a supergravity realisation of inflation. This is of crucial importance if one look at supergravity as the bridge connecting the effective field theory of inflation and a possible UV complete theory like string theory. Within a supergravity theory the inflationary dynamics is tightly constrained. I will discuss a particular kind of geometric constraints which arise by considering particular directions on the scalar manifold, namely the ones which are singled out by the process of supersymmetry breaking (the so called sGoldstino’s). As an example I will consider the constraint in the case of N=1, F-term inflation.

We examine the conditions for beaming of the gluonic field sourced by a heavy quark in strongly-coupled conformal field theories, using the AdS/CFT correspondence. Previous works have found that, contrary to naive expectations, it is possible to set up collimated beams of gluonic radiation despite the strong coupling. We show that, on the gravity side of the correspondence, this follows directly (for arbitrary quark motion, and independently of any approximations) from the fact that the string dual to the quark remains unexpectedly close to the AdS boundary whenever the quark moves ultra-relativistically. We also work out the validity conditions for a related approximation scheme that proposed to explain the beaming effect though the formation of shock waves in the bulk fields emitted by the string. We find that these conditions are fulfilled in the case of ultra-relativistic uniform circular motion that motivated the proposal, but unfortunately do not hold for much more gen eral quark trajectories.

We study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)xU(2)xU(1)xU(1) and U(3)xSp(2)xU(1)xU(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models.

A class of hidden sector polystable vector bundles will be presented that, when used in combination with SU(4) heterotic standard model bundles, lead to completely stable string vacua with exactly the particle spectrum of the MSSM with three right-handed neutrino supermultiplets. Threshold corrections, the effective Lagrangian with soft supersymmetry breaking and its scaling under the renormalization group are discussed. It is shown that gauged B-L symmetry and electroweak symmetry are radiatively broken with a small hierarchy over a wide range of initial parameters. Implications of these SU(4) heterotic standard models for the LHC are explored.