Related papers: Givental J-functions, Quantum integrable systems, …

A family of wave solutions to the full Einstein equations in AdS_5 geometry is derived. These background solutions give by duality the response of N=4 SYM at strong coupling to an arbitrary distribution of fast moving external sources for…

Efficient and powerful approaches to the computation of correlation functions involving determinant, sub-determinant and permanent operators, as well as traces, have recently been developed in the setting of ${\cal N}=4$ super Yang-Mills…

We give the N=2 gauged supergravity interpretation of a generic D=4, N=2 theory as it comes from generalized Scherk-Schwarz reduction of D=5, N=2 (ungauged) supergravity. We focus on the geometric aspects of the D=4 data such as the general…

Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli…

We study four dimensional supersymmetric gauge theory on the noncommutative superspace, recently proposed by Seiberg. We construct the gauge-invariant action of N=1 super Yang-Mills theory with chiral and antichiral superfields, which has…

We introduce the description of a Wilson surface as a 2-dimensional topological quantum field theory with a 1-dimensional Hilbert space. On a closed surface, the Wilson surface theory defines a topological invariant of the principal…

We study half-BPS surface operators in N=2 supersymmetric QCD in four dimensions with gauge group SU(2) and four fundamental flavours. We compute the twisted chiral superpotential that describes the effective theory on the surface operator…

We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d ${\cal N} = 4$ superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The…

This is a review article on the quantum toroidal algebras, focusing on their roles in various solvable structures of 2d conformal field theory, supersymmetric gauge theory, and string theory. Using $\mathcal{W}$-algebras as our starting…

In this lecture we give an elementary introduction to the natural realization of non-perturbative N=2 quantum field theories as a low energy limit of classical string theory. We review a systematic construction of six, five, and four…

We compute the gauge field functional integral giving the scalar product of the SU(2) Chern-Simons theory states on a Riemann surface of genus > 1. The result allows to express the higher genera partition functions of the SU(2) WZNW…

In a $\mathcal{N}=2$ superconformal gauge theory with matter hypermultiplets transforming in the symmetric and anti-symmetric representations of SU($N$), we study the integrated correlators of two Coulomb-branch operators and two moment-map…

It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.

Non(anti)commutative gauge theories are supersymmetric Yang-Mills and matter system defined on a deformed superspace whose coordinates obey non(anti)commutative algebra. We prove that these theories in four dimensions with N=1/2…

We consider the four dimensional scale invariant N=2 SU quiver gauge theories with USp(2N) ends or SU(2N) ends with antisymmetric matter representations. We argue that these theories are realized as six dimensional A_{2N-1} (0,2) theories…

We construct the lattice gauge theory of the group G_N, the semidirect product of the permutation group S_N with U(1)^N, on an arbitrary Riemann surface. This theory describes the branched coverings of a two-dimensional target surface by…

In a superspace formulation of Yang-Mills theory previously proposed, we show how gauge-invariant operators and scalars can be incorporated keeping intact the (broken) $Osp(3,1|2)$ symmetry of the superspace action. We show in both cases,…

In this paper the free gauge field theories on a Riemann surface of any genus are quantized in the covariant gauge. The propagators of the gauge fields are explicitly derived and their properties are analysed in details. As an application,…

The theory of the operator $$G(x) = |\underline{x}|^2 \frac{\partial }{\partial x_0} + \underline{x} \sum_{j=1}^n x_j \frac{\partial }{\partial x_j} $$ is deeply associated with the slice monogenic function theory and has grown in recent…

We study 6d N=(2,0) theory of type SU(N) compactified on Riemann surfaces with finite area, including spheres with fewer than three punctures. The Higgs branch, whose metric is inversely proportional to the total area of the Riemann…