Mathematical Aspects of String and MTheory
Wednesday 11th January 2012 to Friday 13th January 2012
09:00 to 09:45  Registration  
09:45 to 10:00  Welcome from John Toland (INI Director) & Annoucements  INI 1  
10:00 to 11:00 
Geometry and Connectedness of Heterotic String Compactifications with Fluxes
I will discuss the geometry of heterotic string compactifications with fluxes. The compactifications on 6 dimensional manifolds which preserve N=1 supersymmetry in 4 dimensions must be complex conformally balanced manifolds which admit a nowwhere vanishing holomorphic (3,0)form, together with a holomorphic vector bundle on the manifold which must admit a Hermitian YangMills connection. The flux, which can be viewed as a torsion, is the obstruction to the manifold being Kahler. I will describe how these compactifications are connected to the more traditional compactifications on CalabiYau manifolds through geometric transitions like flops and conifold transitions. For instance, one can construct solutions by flopping rational curves in a CalabiYau manifold in such a way that the resulting manifold is no longer Kahler. Time permitting, I will discuss open problems, for example the understanding of the the moduli space of heterotic compactifications and the related problem of determining the massless spectrum in the effective 4 dimensional supersymmetric field theory. The study of these compactifications is interesting on its own right both in string theory, in order to understand more generally the degrees of freedom of these theories, and also in mathematics. For instance, the connectedness between the solutions is related to problems in mathematics like the conjecture by Miles Reid that complex manifolds with trivial canonical bundle are all connected through geometric transitions.

INI 1  
11:00 to 11:30  Morning Coffee  
11:30 to 12:30 
M Larfors (LudwigMaximiliansUniversität München) A tendimensional action for nongeometric fluxes
In ten and fourdimensional supergravities, the descriptions of nongeometric configurations are different. In the former, nongeometry arises as naively nonsingle valued supergravity fields. In the latter, new terms, coming from nongeometric Q and Rfluxes, appear in the fourdimensional potential. In this talk, it is shown that a tendimensional field redefinition results in a Qflux term in the NSNS Lagrangian. This change of field basis is inspired by generalized geometry. We argue that this new field basis provides a good description of certain nongeometric configurations. In particular, using the new basis, a dimensional reduction can be performed, in which the Qflux term gives rise to the expected term in the fourdimensional potential. We also discuss the global issues of this setup.

INI 1  
12:30 to 13:30  Lunch at Wolfson Court  
14:00 to 15:00 
Supergravity as generalised geometry
We show how extensions of conventional differential geometry, so called "generalised geometry", give a natural way of formulating type II and elevendimensional supergravity theories, unifying the bosonic fields and symmetries. There is a natural action of the U and Tduality 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 LeviCivita 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.

INI 1  
15:00 to 15:30  Afternoon Tea  
15:30 to 16:30 
Stringy corrections with Bfield
I'll discuss the inclusion of Bfield in the higher derivative corrections in the effective theories, its possible applications and interpretations.

INI 1  
16:30 to 17:30 
Reductions with reduced supersymmetry using generalized geometry
We will discuss reductions of Mtheory 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 Uduality group (i.e., the moduli space metrics), and how they enter in the superpotential.

INI 1  
17:30 to 18:00  Drinks Reception 
10:00 to 11:00 
Dbrane/Oplane effective actions, disc amplitudes and Tduality
I will be discussing the computation of superstring scattering amplitudes in the presence of Dbranes and orientifold planes. The results encode certain terms in the low energy effective actions of spacetime fields localized on branes/planes. I will describe some of these interactions and show how they restore compatibility with Tduality.

INI 1  
11:00 to 11:30  Morning Coffee  
11:30 to 12:30 
Mbranes and String structures
I will describe the relation of the Cfield to String structures, which are essentially Spin structures on loop space, and explain how these structures capture certain geometric and topological aspects of Mbranes.

INI 1  
12:30 to 13:30  Lunch at Wolfson Court  
14:00 to 15:00 
T Hartman (Institute for Advanced Study, Princeton) Higher Spin Gravity and 2d CFTs
Higher spin gravity in three dimensions is holographically dual to a twodimensional CFT with extended conformal symmetry, known as a Walgebra. This raises the possibility of tackling difficult questions in holography or quantum gravity by exploiting the Walgebra to do exact computations at all values of the coupling. I will review the status of various higher spin dualities, and for the case of AdS_3, describe the detailed matching of the spectrum and the CFT interpretation of higher spin black holes.

INI 1  
15:00 to 15:30  Afternoon Tea  
15:30 to 16:30 
E Diaconescu (Rutgers, The State University of New Jersey) Lagrangian cycles and knots at large N
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.

INI 1  
16:30 to 17:30 
Line bundle Standard Models
I will discuss recent work constructing heterotic standard models by compactifying on smooth CalabiYau threefolds in the presence of purely Abelian internal gauge fields. The simple construction of these models allows for a largescale, algorithmic approach to the study of heterotic string vacua. In particular, a systematic search over complete intersection CalabiYau manifolds with less than six Kahler parameters has lead to over 1000 such models with exact Standard Model spectra. In addition, the presence of additional global U(1) symmetries, leads to a rich variety of geometric/phenomenological structures and provides a window into a larger moduli space of nonAbelian vector bundles.

INI 1  
19:30 to 22:00  Conference Dinner at Emmanuel College 
10:00 to 11:00 
V Pestun (Institute for Advanced Study, Princeton) Instanton calculus in quiver gauge theories 
INI 1  
11:00 to 11:30  Morning Coffee  
11:30 to 12:30 
String Theory and the Moonshine Programme
In some occasions, certain finite groups display a close connection to certain modular objects defined on the upperhalf plane. The most wellknown of such a relation between these two distinct mathematical structures is the socalled monstrous moonshine, relating the largest sporadic group to a set of modular functions. String theory, with its power to geometrise automorphic objects, has been proven instrumental in providing insights into these mysterious relations. Recently, certain unexpected relation with various similarities to the monstrous moonshine has been discovered. In this talk I will review these recent mathematical developments, while putting extra focus on the role played by string theory.

INI 1  
12:30 to 13:30  Lunch at Wolfson Court  
14:00 to 15:00 
Wallcrossing, dilogarithm identities and the QK/HK correspondence
I will explain how the wallcrossing behaviour of Dbrane instantons in type II CalabiYau compactifications is captured by a certain hyperholomorphic line bundle over a hyperkähler manifold. This construction relies on a general duality between 4ndimensional quaternionKähler and hyperkähler spaces with certain continuous isometries. The continuity of the moduli space metric across walls of marginal stability is encoded in nontrivial identities for the Rogers dilogarithm, which are shown to be a consequence of the motivic KontsevichSoibelman wallcrossing formula. Finally, I will offer some speculations on how the construction is modified in the presence of NS5brane effects.

INI 1  
15:00 to 15:30  Afternoon Tea  
15:30 to 16:30 
L Hollands ([CALTECH]) A 4d2d correspondence for Sicilian quivers
In the last few years a wealth of novel properties of N=2 supersymmetric gauge theories has been uncovered. In particular, much has been learned about the strong coupling limits of these gauge theories through a dual twodimensional perspective in terms of Riemann surfaces. In this talk I will discuss a quantitative check of this 4d2d correspondence by computing the instanton partition function of an SU(2) gauge theory that is associated to a higher genus Riemann surface and its corresponding conformal block. This exercise will reveal a better understanding of the correspondence between fourdimensional instanton partition functions and twodimensional conformal blocks.

INI 1  
16:30 to 17:30 
A Dabholkar (Laboratoire de Physique Théorique et Hautes Energies) Localization and Exact Quantum Entropy of Black Holes 
INI 1 