Related papers: Recent developments in 2d $\mathcal{N} = (2,2)$ su…
We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal…
We study N=2 supersymmetric U(1) gauge theory in the noncommutative harmonic superspace with nonanticommutative fermionic coordinates. We examine the gauge transformation which preserves the Wess-Zumino gauge by harmonic expansions of…
We propose a general way to complete supersymmetric theories with operators below the unitarity bound, adding gauge-singlet fields which enforce the decoupling of such operators. This makes it possible to perform all usual computations, and…
We show that SU(N) gauge theories in 2+1 dimensions are close to N=\infty for N \geq 2. The dimensionful coupling, g^2, is proportional to 1/N, at large N, confirming the usual diagram-based expectation. Preliminary calculations in 3+1…
We study two-dimensional N=2 supersymmetric actions describing general models of scalar and vector multiplets coupled to supergravity.
We construct 4D $\mathcal{N}=2$ theories on an infinite family of 4D toric manifolds with the topology of connected sums of $S^2 \times S^2$. These theories are constructed through the dimensional reduction along a non-trivial $U(1)$-fiber…
We study the low energy behaviour of N=(2,2) supersymmetric gauge theories in 1+1 dimensions, with orthogonal and symplectic gauge groups and matters in the fundamental representation. We observe supersymmetry breaking in super-Yang-Mills…
We study macroscopically two dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product $\mathbb{T}^{d} \times \mathbb{R}^{2}_{\epsilon}$ of a…
We suggest IR-dual descriptions for d=3 N=2 supersymmetric gauge theories with gauge groups USp(2N_c) and U(N_c) and matter in the fundamental representation. We relate this duality to the IR duality of d=4 N=1 SQCD theories, and in one…
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…
In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to…
We study three dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-Matter theories on the direct product of a circle and a two dimensional hemisphere ($S^1 \times D^2$) with specified boundary conditions by the method of localization.…
A review is given of recent research on two-dimensional gauge theories, with particular emphasis on the equivalence between these theories and certain string theories with a two-dimensional target space. Some related open problems are…
In the last six years remarkable developments have taken place concerning the representation theory of N=2 superconformal algebras. Here we present the highlights of such developments.
We give a pedagogical review of the localization of supersymmetric gauge theory on 5d toric Sasaki-Einstein manifolds. We construct the cohomological complex resulting from supersymmetry and consider its natural toric deformations with all…
We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The…
Recent work on the numerical solution of supersymmetric gauge theories is described. The method used is SDLCQ (supersymmetric discrete light-cone quantization). An application to N=1 supersymmetric Yang-Mills theory in 2+1 dimensions at…
We consider general aspects of N=2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U(1) gauge theories, we discuss the quantum corrections to the moduli space, and…
In this paper we explore some of the features of large N supersymmetric and nonsupersymmetric gauge theories using Maldacena's duality conjectures. We shall show that the resulting strong coupling behavior of the gauge theories is…
Starting with the prepotential description of two-dimensional $(2,2)$ supergravity we use local supersymmetry transformations to go to light-cone gauge. We discuss properties of the theory in this gauge and derive Ward identities for…