Sergei Alexandrov: D-instantons, Quantum mirror symmetry and Integrability
I'll present recent results on the non-perturbative description
of the hypermultiplet moduli space of compactified Type II string theory.
The geometry of the moduli space gets instanton corrections due to
D-branes and I'll show how one can describe all these D-instantons
using the twistor approach to quaternionic geometries.
These results are used to get a quantum completion of the classical
mirror map and to show a deep relation of the twistor description
of D-instantons to integrability.
Serguei Barannikov: gl(N)-equivariant matrix models, compactified moduli spaces of curves and
cyclic cohomology
I'll review my higher dimensional generalisation of matrix Airy
integrals, which gives gl(N)-equivariantly closed matrix models starting
from Calabi-Yau categories, and produces natural generating functions of
cohomology classes of compactified moduli spaces of curves.
I'll mention how my integrals fit into a new kind of cohomology theory of
associative algebras, which incorporates the cyclic cohomology and the
nc-BV differential. Lastly, I'll discuss the computational aspects:
localization and tau-functions.
Marco Baumgartl: D-Brane Superpotentials: A Worldsheet Perspective
We explain how superpotentials can be obtained with worldsheet methods in
topological string theory. From the worldsheet perspective, the superpotential
of a D-brane wrapping internal cycles of a Calabi-Yau manifold is given as a
generating functional for disk correlation functions. On the other hand, from
the geometric point of view, D-brane superpotentials are captured by certain
chain integrals. We present recent results which show how these two approaches
are related. In particular we show that worldsheet correlators in
Landau-Ginzburg theories computed in the matrix factorizations description can
be explicitly identified with lowest level expansion terms of relative period
integrals.
Alexander Belavin: Two dimensional gravity in Liouville and Matrix Model
approaches
I will talk about three different appraches to 2d Gravity.
The first one is the continuous approach, in which the theory is defined
through the functional integral over the Riemannian metric with appropriate
gauge fixing.The choice of the conformal gauge leads to quantum Liouville theory
and for that reason this approach is often called the Liouville Gravity.
The second one is the discrete approach, based
on the idea of approximating the fluctuating 2d geometry by an
ensemble of planar graphs, so that the continuous theory is
recovered in the scaling limit.
The discrete approach is usually referred to as the Matrix Models.
The third approach is Witten-Kontsevich topological gravity or
Intersection theory on the moduli space of Riemann surfaces.
Since the end of 80's there exist the conjecture that all
three models are identical.However in literal sense it is not true. I will show
in what namely sense they are are equivalent.
Andrea Brini: Open topological strings and integrable hierarchies: remodeling the
A-model
In recent years several techniques inspired by string duality have been put
forward to solve the topological A-model on toric Calabi-Yau threefolds,
either via large N duality with Chern-Simons theory (the topological vertex) or
using mirror symmetry and matrix-model-inspired techniques (the
"Remodeled-B-Model"). I will build on recent progress in the mathematical
theory of open Gromov-Witten invariants to propose, in purely A-model terms, a
new formalism to compute open string amplitudes on these target spaces.
In this framework, localization formulae relate D-brane amplitudes to closed
string amplitudes perturbed with twisted masses through an analogue of the "loop
insertion operator" of matrix models; the connection of the closed model to tau
functions of 1+1 integrable hierarchies allows in turn an effective computation
of the amplitudes, as well as an A-model derivation of several known results
from mirror symmetry (e.g. the spectral curves). This is work in progress,
partly based on previous joint work with R. Cavalieri (arXiv:1007.0934).
Xenia de la Ossa: Arithmetic of Calabi-Yau Manifolds
TBA
Nadav Drukker: Observables in 4d N=2 theories and 2d conformal
Toda theories
Thomas Grimm: Couplings in effective 4d Supergravity Actions from higher Dimensions
TBA
Shinobu Hikami: Duality and replicas for a unitary matrix model
In a generalized Airy matrix model, a power p replaces the cubic term of
the Airy model introduced by Kontsevich. The parameter p corresponds to
Witten's spin index in the theory of intersection numbers of moduli space of
curves. A continuation in p down to p = -2 yields a well studied unitary matrix model.
The application of duality and replica to the p-th Airy model provides,
through this equivalence, a generating function for both the weak and
the strong coupling expansions of the unitary model.
We thereby recover and extend further the results for
these expansions. This is a joint work with E. Brezin (arXiv:1005.4730).
Amir Kashani-Poor: A matrix model for the topological string
on arbitrary toric Calabi-Yau manifolds
I will introduce a matrix model which reproduces the topological string partition function on any given toric Calabi-Yau manifold. By the BKMP conjecture, its spectral curve should be symplectically equivalent to the mirror curve of the Calabi-Yau geometry. I will discuss the derivation of this result.
Christoph Keller: Siegel modular forms and CFT partition
functions at genus two
The genus two partition function of a chiral self-dual CFT is a Siegel
modular form.
It is explained how this implies infinitely many relations among
the structure constants of the theory. We then show how these
relations are a consequence
of the associativity of the OPE, as well as the modular covariance properties
of the torus one-point functions. Using these techniques we prove that for the
proposed extremal conformal field theories at c = 24k a consistent
genus two vacuum
amplitude exists for all k, but that this does not actually check the
consistency of
these theories beyond what is already testable at genus one.
Albrecht Klemm: Topological string theory, BPS counting and modular forms
TBA
Semyon Klevtsov: Kahler metrics, 2d gravity and complex random matrices
We consider the problem of integration over 2d metrics from the point of view
of the Kahler gauge. We discuss the role of the Mabuchi K-energy in this
context, relation to Liouville theory, and to the large N limit of a complex
matrix model. Finally, we discuss finite dimensional approximations to the 2d
gravity measure, using Bergman metrics. Based on work in progress with S.
Zelditch and F. Ferrari
Jan Manschot: From N=4 SYM on P2 to a generalized Rademacher expansion
The spectrum of topologically twisted N=4 SYM on a surface is closely related to the moduli
space of stable coherent sheaves. Yoshioka computed generating
functions of Poincare polynomials of such moduli spaces if the
surface is P2 and the rank of the sheaves is 2. Motivated by
S-duality of N=4 supersymmetric Yang-Mills, this talk will discuss the modular properties of
these
generating functions. Based on this, we prove a conjecture by Vafa and Witten, which
expresses
the generating functions of Euler numbers as a mixed mock modular
form. Moreover, we derive an exact formula for the Fourier coefficients of this function,
which is similar to the Rademacher expansion for weakly holomorphic modular
forms but is more complicated.
Marcos Marino: Lectures on non-perturbative effects in large N theory,
matrix models and topological strings
Bengt Nilsson: Higgsing of topologically gauged M2-branes
We will discuss how to couple superconformal theories for M2-branes with 8 or 6 supersymmetries
to superconformal gravity. The ABJM type theories are then Higgsed in order to relate them to D2-brane theories. We
find that these end up sitting at a chiral point in the sense of Li, Song and Strominger.
Boris Pioline: Five-brane instantons, topological
wave functions and hypermultiplets
TBA
Alexandr Popolitov: On relation between Nekrasov functions and BS periods in pure SU(N) case
We investigate the duality between the Nekrasov function and the
quantized Seiberg-Witten prepotential. We concentrate on providing more thorough checks than the
ones presented by Morozov and Mironov in their paper and do not discuss the motivation and
historical context of this duality. The check of the conjecture up to $o (\hbar^6, \ln (\Lambda))$
is done by hands for arbitrary $N$ (explicit formulas are presented). Moreover, details of the
calculation that are essential for the computerization of the check are worked out. This allows us
to test the conjecture up to $\hbar^6$ and up to higher powers of $\Lambda$ for $N = 2,3,4$. Only
the case of pure SU(N) gauge theory is considered.
Pavel Putrov: ABJM theory and topological strings
I will describe how one can calculate certain quantities in the ABJM
theory using techniques of matrix models and topological strings. Some
results provide explicit checks of the AdS_4/CFT_3 conjecture.
Ricardo Schiappa: Large-Order Behavior in Matrix Models and Topological Strings
I will review recent work in relating non-perturbative instanton effects to the
large-order behavior of perturbation theory, within the context of matrix models and topological
strings.
Piotr Sulkowski: Wall-crossing, free fermions and matrix models
I will describe wall-crossing phenomena in a system of D6-D2-D0 bound
states on a class of local, toric manifolds, and represent them in a
free fermion formalism. Using this formalism I will construct matrix
models encoding degeneracies of these D6-D2-D0 bound states and
discuss their properties, in particular a relation to the remodeling
conjecture.
Don Zagier: Properties of Modular Forms and their Asymptotics