Related papers: N=1 G_2 SYM theory and Compactification to Three D…
In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2) gauge theory…
Using matrix-model methods we study three different N=2 models: U(N) x U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find…
We study the $N=1$ supersymmetric $G_2$ gauge theories with $N_f$ flavors of quarks in the fundamental vector representation. We find dynamically generated superpotentials, smooth quantum moduli space, quantum moduli space with additional…
We study exact effective superpotentials of four-dimensional {\cal N} = 2 supersymmetric gauge theories with gauge group U(N) and various amounts of fundamental matter on R^3 x S^1, broken to {\cal N} = 1 by turning on a classical…
We describe how the ingredients and results of the Seiberg-Witten solution to N=2 supersymmetric U(N) gauge theory may be obtained from a matrix model.
The matrix model computations of effective superpotential terms in N=1 supersymmetric gauge theories in four dimensions have been proposed to apply more generally to gauge theories in higher dimensions. We discuss aspects of…
We compute the ${\cal N}=2$ supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the K\"ahler form with jumps…
We introduce in this paper two dimensional lattice models whose continuum limit belongs to the $N=2$ series. The first kind of model is integrable and obtained through a geometrical reformulation, generalizing results known in the $k=1$…
We derive the three-dimensional $\mathcal{N}=1$ effective theories obtained by compactifying all five ten-dimensional string theories on generic seven-dimensional manifolds with $G_2$ structure. The resulting flux compactifications are…
We present a systematic study of N=1 supersymmetric gauge theories which are in the Coulomb phase. We show how to find all such theories based on a simple gauge group and no tree-level superpotential. We find the low-energy solution for the…
We construct a three dimensional deconfinement method which enables us to find new three-dimensional dualities and we apply various techniques developed in four dimensional supersymmetric gauge theories, such as the product gauge groups and…
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 present an explicit construction of the factorization of Seiberg-Witten curves for N=2 theory with fundamental flavors. We first rederive the exact results for the case of complete factorization, and subsequently derive new results for…
In this talk I review the structure of vacua of N=2 theories broken down to N=1 and it's link with factorization of Seiberg-Witten curves. After an introduction to the structure of vacua in various supersymmetric gauge theories, I discuss…
We propose a new integrable N=2 supersymmetric Toda lattice hierarchy which may be relevant for constructing a supersymmetric one-matrix model. We define its first two Hamiltonian structures, the recursion operator and Lax--pair…
We discuss recent progress in the understanding of the vacuum structure (effective superpotentials) of confining gauge theories with N=1 supersymmetry. Even for non-supersymmetric theories, appropriate perturbative calculations (e.g. using…
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…
Four dimensional N=2 generalized superconformal field theory can be defined by compactifying six dimensional (0,2) theory on a Riemann surface with regular punctures. In previous studies, gauge coupling constant space is identified with the…
We show how certain non-perturbative superpotentials W, which are the two-dimensional analogs of the Seiberg-Witten prepotential in 4d, can be computed via geometric engineering from 4-folds. We analyze an explicit example for which the…
We study the structure of the moduli spaces of vacua and superpotentials of N=2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum…