Related papers: Seiberg-Witten Toda Chains and N=1 SQCD
We consider 4d and 5d N=2 supersymmetric theories and demonstrate that in general their Seiberg-Witten prepotentials satisfy the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. General proof for the Yang-Mills models (with matter in…
It has been recently shown that the celebrated SCFT$_4$/VOA$_2$ correspondence can be bridged via three-dimensional field theories arising from a specific R-symmetry twisted circle reduction. We apply this twisted reduction to the…
The lack of any local solution to the first-order-in-h omegamn Seiberg-Witten (SW) map equations for U(1) vector superfields compels us to obtain the most general solution to those equations that is a quadratic polynomial in the ordinary…
We show that in the perturbative regime defined by the coupling constant, the theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with or without Supersymmetry-- gives an ordinary gauge theory which is, at the quantum…
We declare briefly several interesting features of the quantum relativistic Toda chain at N-th root of unity. We consider the finite dimensional representation of the Weyl algebra. The origin of the features mentioned is that we consider…
A number of formulas are displayed concerning Whitham theory for a simple example of pure N=2 susy YM with gauge group SU(2). In particular this serves to illuminate the role of Lambda and T derivatives and the interaction with…
We discuss the mass-deformed N=4 SU(N) supersymmetric Yang-Mills theory (also known as the N=1* theory). We analyze how the correlation functions of this theory transform under S-duality, and which correlation functions depend…
This paper discusses in a systematical way exact retarded solutions to the classical SU(N) Yang-Mills equations with the source composed of several colored point particles. A new method of finding such solutions is reviewed. Relying on…
We obtain the Seiberg-Witten geometry for four-dimensional N=2 gauge theory with gauge group SO(2N_c) (N_c \leq 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N=2 $E_6$ theory with…
It is argued that there are strong similarities between the infra-red physics of N=2 supersymmetric Yang-Mills and that of the quantum Hall effect, both systems exhibit a hierarchy of vacua with a sub-group of the modular group mapping…
In this article we explore the duality between the low energy effective theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1. The theories we study are the five-dimensional uplifts of…
We identify the spectral curve of pure gauge SU(2) Seiberg-Witten theory with the Weierstrass curve $\mathbbm{C}/L \ni z \mapsto (1,\wp(z),\wp(z)')$ and thereby obtain explicitely a modular form from which the moduli space parameter $u$ and…
Seiberg-Witten geometry of mass deformed $\mathcal N=2$ superconformal ADE quiver gauge theories in four dimensions is determined. We solve the limit shape equations derived from the gauge theory and identify the space $\mathfrak M$ of…
We propose a number of new Seiberg dualities of N=1 quiver gauge theories. The new Seiberg dualities originate in new S-dualities of N=2 superconformal field theories recently proposed by Gaiotto. N=2 S-dual theories deformed by suitable…
We present preliminary results of a study of the supersymmetric (SUSY) Ward identities (WIs) for the N=1 SU(2) SUSY Yang-Mills theory in the context of one-loop lattice perturbation theory. The supersymmetry on the lattice is explicitly…
Recently N. Seiberg has shown that certain N=1 supersymmetric Yang -- Mills theories have the property that their infrared physics can be equivalently described by {\it two different} gauge theories, with the strong coupling region of one…
We show how the method of separation of variables can be used to construct integrable models corresponding to curves describing vacuum structure of four-dimensional ${\cal N} = 2$ SUSY Yang-Mills theories. We use this technique to construct…
Detailed studies of four dimensional N=2 superconformal field theories (SCFT) defined by isolated complete intersection singularities are performed: we compute the Coulomb branch spectrum, Seiberg-Witten solutions and central charges. Most…
Noncommutative versions of theories with a gauge freedom define (when they exist) consistent deformations of their commutative counterparts. General aspects of Seiberg-Witten maps are discussed from this point of view. In particular, the…
We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on…