# Workshop Programme

## for period 11 - 13 January 2012

### Mathematical Aspects of String and M-Theory

11 - 13 January 2012

Timetable

Wednesday 11 January | ||||

09:00-09:45 | Registration | |||

09:45-10:00 | Welcome from John Toland (INI Director) & Annoucements | |||

10:00-11:00 | de la Ossa, X (University of Oxford) |
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Geometry and Connectedness of Heterotic String Compactifications with Fluxes | Sem 1 | |||

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 now-where vanishing holomorphic (3,0)-form, together with a holomorphic vector bundle on the manifold which must admit a Hermitian Yang-Mills 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 Calabi-Yau manifolds through geometric transitions like flops and conifold transitions. For instance, one can construct solutions by flopping rational curves in a Calabi-Yau 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. |
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11:00-11:30 | Morning Coffee | |||

11:30-12:30 | Larfors, M (Ludwig-Maximilians-Universität München) |
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A ten-dimensional action for non-geometric fluxes | Sem 1 | |||

In ten- and four-dimensional supergravities, the descriptions of non-geometric configurations are different. In the former, non-geometry arises as naively non-single valued supergravity fields. In the latter, new terms, coming from non-geometric Q- and R-fluxes, appear in the four-dimensional potential. In this talk, it is shown that a ten-dimensional field redefinition results in a Q-flux 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 non-geometric configurations. In particular, using the new basis, a dimensional reduction can be performed, in which the Q-flux term gives rise to the expected term in the four-dimensional potential. We also discuss the global issues of this set-up. |
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12:30-13:30 | Lunch at Wolfson Court | |||

14:00-15:00 | Waldram, D (Imperial College London) |
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Supergravity as generalised geometry | Sem 1 | |||

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. |
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15:00-15:30 | Afternoon Tea | |||

15:30-16:30 | Minasian, R (CEA/Saclay) |
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Stringy corrections with B-field | Sem 1 | |||

I'll discuss the inclusion of B-field in the higher derivative corrections in the effective theories, its possible applications and interpretations. |
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16:30-17:30 | Graña, M (CEA/Saclay) |
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Reductions with reduced supersymmetry using generalized geometry | Sem 1 | |||

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. |
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17:30-18:00 | Drinks Reception |

Thursday 12 January | ||||

10:00-11:00 | Becker, K (Texas A&M University) |
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D-brane/O-plane effective actions, disc amplitudes and T-duality | Sem 1 | |||

I will be discussing the computation of superstring scattering amplitudes in the presence of D-branes and orientifold planes. The results encode certain terms in the low energy effective actions of space-time fields localized on branes/planes. I will describe some of these interactions and show how they restore compatibility with T-duality. |
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11:00-11:30 | Morning Coffee | |||

11:30-12:30 | Sati, H (University of Pittsburgh) |
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M-branes and String structures | Sem 1 | |||

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. |
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12:30-13:30 | Lunch at Wolfson Court | |||

14:00-15:00 | Hartman, T (Institute for Advanced Study, Princeton) |
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Higher Spin Gravity and 2d CFTs | Sem 1 | |||

Higher spin gravity in three dimensions is holographically dual to a two-dimensional CFT with extended conformal symmetry, known as a W-algebra. This raises the possibility of tackling difficult questions in holography or quantum gravity by exploiting the W-algebra 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. |
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15:00-15:30 | Afternoon Tea | |||

15:30-16:30 | Diaconescu, E (Rutgers, The State University of New Jersey) |
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Lagrangian cycles and knots at large N | Sem 1 | |||

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. |
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16:30-17:30 | Anderson, L (Harvard University) |
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Line bundle Standard Models | Sem 1 | |||

I will discuss recent work constructing heterotic standard models by compactifying on smooth Calabi-Yau three-folds in the presence of purely Abelian internal gauge fields. The simple construction of these models allows for a large-scale, algorithmic approach to the study of heterotic string vacua. In particular, a systematic search over complete intersection Calabi-Yau 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 non-Abelian vector bundles. |
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19:30-22:00 | Conference Dinner at Emmanuel College |

Friday 13 January | ||||

10:00-11:00 | Pestun, V (Institute for Advanced Study, Princeton) |
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Instanton calculus in quiver gauge theories | Sem 1 | |||

11:00-11:30 | Morning Coffee | |||

11:30-12:30 | Cheng, M (Harvard University) |
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String Theory and the Moonshine Programme | Sem 1 | |||

In some occasions, certain finite groups display a close connection to certain modular objects defined on the upper-half plane. The most well-known of such a relation between these two distinct mathematical structures is the so-called 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. |
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12:30-13:30 | Lunch at Wolfson Court | |||

14:00-15:00 | Persson, D (Chalmers University of Technology) |
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Wall-crossing, dilogarithm identities and the QK/HK correspondence | Sem 1 | |||

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. |
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15:00-15:30 | Afternoon Tea | |||

15:30-16:30 | Hollands, L (Caltech) |
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A 4d-2d correspondence for Sicilian quivers | Sem 1 | |||

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 two-dimensional perspective in terms of Riemann surfaces. In this talk I will discuss a quantitative check of this 4d-2d 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 four-dimensional instanton partition functions and two-dimensional conformal blocks. |
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16:30-17:30 | Dabholkar, A (Laboratoire de Physique Théorique et Hautes Energies) |
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Localization and Exact Quantum Entropy of Black Holes | Sem 1 |