Scientific program

All talks will be given in room 05, ground floor at SISSA.

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Monday 17
10:00-11:00	M. Piatek	Liouville theory, N=2 gauge theories and accessory parameters
11:00-11:30	Coffee Break
11:30-12:30	F. Morales	U-folds from hyperelliptic geometries
	Lunch Break
14:30-15:30	S. Cremonesi	Spherical partition functions of N = (2,2) gauge theories and vortices
15:30-16:00	Coffee Break
16:00-17:00	Discussion session
Tuesday 18
10:00-11:00	R. Poghossian	Two-dimensional renormalization group flows revisited
11:00-11:30	Coffee Break
11:30-12:30	S. Pasquetti	Holomorphic blocks in 3d
	Lunch Break
14:30-15:30	F. Passerini	Vortex loop operators in supersymmetric 3d theories
15:30-16:00	Coffee Break
16:00-17:00	Discussion session
Wednesday 19
10:00-11:00	M. Yamazaki	Domain Walls and Their Gravity Duals
11:00-11:30	Coffee Break
11:30-12:30	M. Taki	Generalized Whittaker states and AGT correspondence
	Lunch Break
14:30-15:30	Brini, A.	The remodeled-A model and torus knots at large N
15:30-16:00	Coffee Break
16:00-17:00	Discussion session
Thursday 20
10:00-11:00	M. Billo'	Instanton corrections in N=2 gauge/gravity correspondence
11:00-11:30	Coffee Break
11:30-12:30	Jaskolski, Z.	SuperLiouville - Liouville duality and reflection map
	Lunch Break
14:30-15:30	S. Razamat	Bootstrapping the N=2 superconformal index
15:30-16:00	Coffee Break
16:00-17:00	Discussion session
Friday 21
10:00-11:00	Sulkowski, P.	Knot homologies, super-A-polynomial, and 3d gauge theories
11:00-11:30	Coffee Break
11:30-12:30	Del Zotto, M.	N=2 Arnold's superconformal gauge theories and 2d/4d correspondences
	Lunch Break
14:30-15:30	Wyllard, N.	N=2 from N=2
15:30-16:00	Coffee Break
16:00-17:00	Discussion session

List of Abstracts

Billo', M. -- "Instanton corrections in N=2 gauge/gravity correspondence" -- Abstract: We consider a simple brane set-up supporting N=2 SYM in d=4, consisting of fractional D3 branes at a Z2 orbifold singularity. In this setting we show explicitly how the inclusion of D-instanton effects leads to the non-perturbative modification of the profile of the corresponding gravitational solution. We focus on the twisted scalar which, at the perturbative level, is identified with the gauge coupling. The exact solution we get agrees with what can be guessed via duality to IIA D4/NS5 configurations plus M-theory uplift. Furthermore, we elaborate on the relation between the twisted scalar profile and the gauge theory coupling matrix, which in the exact description is more complicated and intriguing than it appears at the perturbative level.

Brini, A. -- "The remodeled-A model and torus knots at large N" -- Abstract: 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). I will also discuss how this framework can be extended to provide a large N dual description of torus knots inside lens spaces. This talk is based on arXiv:1102.0281 and on work in progress with Tom Coates (Imperial College).

Cremonesi, S. -- Spherical partition functions of N = (2, 2) gauge theories and vortices -- Abstract: I will review the localisation of 2d N = (2, 2) supersymmetric gauge theories with a vector U(1) R-symmetry on the round 2-sphere, leading to a matrix integral expression for the partition function, in the so called "Coulomb branch" representation. For gauge theories which are completely Higgsed in the presence of a Fayet-Iliopoulos term, an alternative localization scheme yields the "Higgs branch" representation of the same partition function as the product of vortex times antivortex partition functions, weighted by semiclassical factors and summed over isolated vacua on the Higgs branch. Finally, I will briefly overview the potential of these exact results for the study of type II string compactifications and supersymmetric gauge theories in various dimensions. Based on arXiv:1206.2356 with F. Benini.

Del Zotto, M. -- "N=2 Arnold's superconformal gauge theories and 2d/4d correspondences"-- Abstract: I will review the relation in between singularity theory, 4d N=2 superconformal field theories arising from type II B geometric engineering on singular 3-folds, and representation theory of 3 CY algebras. Many properties of these theories are captured by a 2d/4d correspondence, in particular, the 2d RG flow may be used to keep under mild control the problem of non-completeness, for models with small modality. The construction yelds the prediction of new periodic Y-systems of TBA type, that are conjectured to correspond to (still unknown) 2d integrable models. Partly based on arXiv:1006.3435, arXiv:1107.5747, arXiv:1110.3826.

Jaskolski, Z. -- "SuperLiouville - Liouville duality and reflection map" -- Abstract: TBA

Morales, F -- U-folds from hyperelliptic geometries -- Abstract: We construct exact supersymmetric solutions of type IIB supergravity associated to D3,D7 systems non-perturbatively completed by D-instantons. Solutions are characterized by a set of holomorphic functions on a plane with non-trivial U-duality monodromies. In the simplest setting, solutions can be thought as generalizations of F-theory, where the torus fiber is replaced by a genus two surface with periods encoding the information about the axio-dilaton, warp factor and NSNS/RR fluxes.

Pasquetti, S. -- Holomorphic blocks in 3d -- Abstract: TBA

Passerini, F. -- Vortex loop operators in supersymmetric 3d theories -- Abstract: Three dimensional gauge theories admit defect disorder line operators, dubbed vortex loop operators.  In this talk I will describe a few properties of this class of operators in the context of supersymmetric theories.

Piatek, M. -- "Liouville theory, N=2 gauge theories and accessory parameters" -- Abstract: The so-called problem of accessory parameters and its relation to Liouville theory and uniformization of the punctured Riemann sphere shall be discussed. In particular, the computation of the unknown accessory parameter of the Fuchsian uniformization of the four-punctured sphere shall be presented. This calculation exploits the relation between the semiclassical limit of quantum Liouvile theory and the Nekrasov-Shatashvili limit of the N=2, U(2) super Yang-Mills theories. Finally, a brief overview of the problems that are still remaining to be opened issues will be demonstrated.

R. Poghossian -- Two-dimensional renormalization group flows revisited -- Abstract: TBA

Ramazat, S. -- Bootstrapping the N=2 superconformal index -- Abstract: We will discuss several aspects of the superconformal index of N=2 theories. In particular we will argue that assuming the validity of dualities interconnecting theories of class S the index of the theories in this class is  completely fixed.  As a by-product of our analysis we will discuss a connection between the computation of the index and integrable models.

Sulkowski, P. -- Knot homologies, super-A-polynomial, and 3d gauge theories -- Abstract: In this talk I will introduce the notion of super-A-polynomial, and present its various physical and mathematical properties. Super-A-polynomial is a new invariant of knots that provides a two-parameter deformation of an ordinary A-polynomial, and in particular it encodes information about categorification/refinement of the HOMFLY polynomial. On the physics side, in 3d N=2 theories related by 3d-3d duality to knots, super-A-polynomial plays an analogous role to the Seiberg-Witten curve in 4d theories; its analysis reveals new dualities between 3d theories, interesting singularity structure, flavor symmetry enhancement, etc.

Taki, M. -- Generalized Whittaker states and AGT correspondence -- Abstract: The AGT relation for 4d asymptotically-gauge theories is the equivalence between instanton partition functions and irregular conformal blocks. The irregular conformal blocks are defined by using irregular states, which are certain extension of the primary states of 2d CFT. In this talk we construct these irregular states explicitly. We use the AGT correspondence as the base of the idea. Then we find that in 2d CFT there exists an extended version of coherent state as a natural object, and this object plays a key role to establish the AGT correspondence for wider classes of 4d theories.

Yamazaki, M. -- "Domain Walls and Their Gravity Duals" -- Abstract: In this talk I will describe the 3d supersymmetric domain wall theories, their roles in various dualities and their gravity duals, partly based on my papers arXiv:1105.4390, arxiv:1206.2920.

Wyllard, N. -- N=2 from N=2 -- Abstract: We describe how to compute (irregular) conformal blocks in 2d CFTs whose chiral algebra is the N=2 superconformal algebra using the connection to instanton partition functions in N=2 4d gauge theories. Joint work with V. Belavin, arXiv:1205.3091.