Related papers: Seiberg-Witten Toda Chains and N=1 SQCD
The strongly coupled vacua of an N=1 supersymmetric gauge theory can be described by imposing quantization conditions on the periods of the gauge theory resolvent, or equivalently by imposing factorization conditions on the associated N=2…
We investigate the confining phase vacua of supersymmetric $Sp(2\NC)$ gauge theories that contain matter in both fundamental and antisymmetric representations. The moduli spaces of such models with $\NF=3$ quark flavors and $\NA=1$…
Classical vacuum - pure gauge - solutions of Euclidean two-dimensional SU(2) Yang-Mills theories are studied. Topologically non-trivial vacua are found in a class of gauge group elements isomorphic to $S_2$. These solutions are unexpectedly…
Using Seiberg-Witten theory it is known that the dynamics of N=2 supersymmetric SU(n) Yang-Mills theory is determined by a Riemann surface. In particular the mass formula for BPS states is given by the periods of a special differential on…
Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal…
We consider the close relation between duality in N=2 SUSY gauge theories and integrable models. Various integrable models ranging from Toda lattices, Calogero models, spinning tops, and spin chains are related to the quantum moduli space…
We construct dimer graphs for relativistic Toda chains associated with classical untwisted Lie algebras of A, B, C$_0$, C$_\pi$, D types and twisted A, D types. We show that the Seiberg-Witten curve of 5d $\mathcal{N}=1$ pure supersymmetric…
Linear recursion relations for the instanton corrections to the effective prepotential are derived for N=2 supersymmetric gauge theories with one hypermultiplet in the adjoint representation of SU(N) using the Calogero-Moser…
We review recent work on the study of N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on three main results: (i) We develop a new recursive method to compute the whole…
I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances.…
The explicit form of non-Abelian noncommutative supersymmetric (SUSY) chiral anomaly is calculated, the Wess-Zumino consistency condition is verified and the correspondence of the Yang-Mills sector to the previously obtained results is…
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those…
We study the physics of the Seiberg-Witten and Argyres-Faraggi-Klemm-Lerche-Theisen-Yankielowicz solutions of $D=4$, $\mathcal{N}=2$ and $\mathcal{N}=1$ $SU(N)$ supersymmetric gauge theory. The $\mathcal{N}=1$ theory is confining and its…
S-matrices for integrable perturbations of $N=2$ superconformal field theories are studied. The models we consider correspond to perturbations of the coset theory $G_k \times H_{g-h} /H_{k+g-h} $. The perturbed models are closely related to…
I review the appearence of integrable structures in the formulation of exact nonperturbative solutions to $4d$ supersymmetric quantum gauge theories. Various examples of ${\cal N}\geq 2$ SUSY Yang-Mills nonperturbative solutions are…
We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the…
We construct an explicit solution of the Seiberg-Witten map for a linear gauge field on the non-commutative plane. We observe that this solution as well as the solution for a constant curvature diverge when the non-commutativity parameter…
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…
Starting from the Seiberg-Witten solution of N=2 SQCD with the U(N) gauge group and N_f quark flavors we construct the so-called \mu-dual N=1 theory in the r vacua in the regime analogous to that existing to the left of the left edge of the…
The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with matter is analysed as an isomonodromy problem. We show that the holomorphic section describing the effective action can be deformed by moving its singularities on…