Appendix: Complete List of Abstracts |
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3.15.3Boundary Effects on the Interface Dynamics for the Stochastic Allen-Cahn Equation
Stella Brassesco
IVIC, Caracas sbrasses@ivic.ve
We consider a stochastic perturbation of the Allen–Cahn equation in a bounded interval [−a, b] with boundary conditions fixing the different phases at a and b. We
investigate the asymptotic behavior of the front separating the two stable phases in
√
the limit → 0, when the intensity of the noise is and a, b → ∞ with . In particular, we prove that it is possible to choose a = a( ) such that in a suitable time scaling limit, the front evolves according to a one-dimensional diffusion process with a nonlinear drift accounting for a “soft” repulsion from a. We finally show that a “hard” repulsion can be obtained by an extra diffusive scaling.
3.16 String Theory
Organizers N. Berkovits (São Paulo), R. Dijkgraaf (Amsterdam)
3.16.1 Topological Strings and (Almost) Modular Forms
Mina Aganagic
UC Berkeley minamath.berkeley.edu
The mapping class group Γ is a symmetry of the topological string theory on a Calabi-Yau. This symmetry has a natural realization in the quantum theory, and constrains the topological string partition function. The topological string amplitudes are either holomorphic, quasi-modular forms of Γ , or modular forms which are almost holomorphic. Moreover, at each genus, certain combinations of the amplitudes have to be both holomorphic and modular invariant.
3.16.2 Gauge Theory and Link Homologies
Sergei Gukov
Harvard gukovsakharov.physics.harvard.edu
The main goal of this talk is to explain the physical interpretation of the existing link homologies—such as the Khovanov homology or knot Floer homology—and to propose their various generalizations motivated from physics. In particular, starting with a brief introduction into knot homology theories, I will describe a frame-
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YRS and XV ICMP |
work for unifying the sl(N) Khovanov-Rozansky homology (for all N) with the knot Floer homology. This unification, based on the interpretation in topological string theory, is accomplished by a new triply graded homology theory which categorifies the HOMFLY polynomial. Further insights can be obtained by realizing knot homologies in gauge theory. As I will explain in the main part of the talk, surface operators in gauge theory and braid group actions on categories play an important role in such realizations.
3.16.3 Non-Geometric String Backgrounds
Chris Hull
Imperial College c.hullimperial.ac.uk
In string theory, the standard field theory symmetries of diffeomorphisms and gauge symmetries are augmented by stringy duality symmetries that have no field theory analogue. Conventional spacetime manifolds are constructed from local patches equipped with a metric and gauge and matter fields, and these are glued together using diffeomorphisms and gauge symmetries. In string theory there is the possibility of also using duality symmetries to glue together local spacetime patches, resulting in a “non-geometric background” that has no conventional geometric description. This suggests that in string theory the conventional geometric spacetime picture should be replaced by something more general, allowing a much wider class of string theory backgrounds than has hitherto been considered. The purpose of this talk is to explore such non-geometric backgrounds and some of their implications.
3.16.4Topological Reduction of Supersymmetric Gauge Theories and S-Duality
Anton Kapustin
Caltech kapustintheory.caltech.edu
I discuss topological and semi-topological reduction of N = 4 and N = 2 field theories on a Riemann surface. In the N = 4 case, this relates S-duality of 4d gauge theories with mirror symmetry of the Hitchin moduli space. In the N = 2 case, the reduction yields a half-twisted sigma-model with Hitchin moduli space as a target.
3.16.5 Phase Transitions in Topological String Theory
Marcos Marino Beiras
CERN
Marcos.Marino.Beirascern.ch
Appendix: Complete List of Abstracts |
863 |
Topological strings in Calabi–Yau manifolds undergo phase transitions at small distances that signal the onset of quantum geometry. In this talk, after a brief review, I analyze this phenomenon when the Calabi–Yau is a bundle over a sphere. Mathematically, this theory can be regarded as a deformation of Hurwitz theory. The resulting models exhibit critical behavior, but the universality class of the transition corresponds to pure 2d gravity, and one can define a double–scaled theory at the critical point which is governed by the Painleve I equation. It is also possible to induce multicritical behavior. I will also comment on the implications of this result for the conjectural nonperturbative completion of these models.
3.16.6 Hyper-Multiplet Couplings in N = 2 Effective Action
Pierre Vanhove
CEA Saclay pierre.vanhovecea.fr
We will address the analysis of the quantum corrections to the hypermultiplet geometry of N = 2 supergravity, with some emphasis on the case of the of universal (dilaton) hypermutiplet. We will discuss some special contributions to the N = 2 effective action in the hypermultiplet sector from higher-genus string theory amplitude computation.