Related papers: Penner Type Matrix Model and Seiberg-Witten Theory
The Seiberg-Witten solution plays a central role in the study of N=2 supersymmetric gauge theories. As such, it provides a proving ground for a wide variety of techniques to treat such problems. In this review we concentrate on the role of…
We discuss gauge theory with a topological N=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space $\cal M$ and the partition function equals the Euler number of $\cal M$. We explicitly…
The relation between the Seiberg-Witten prepotentials, Nekrasov functions and matrix models is discussed. We derive quasiclassically the matrix models of Eguchi-Yang type, describing the instantonic contribution to the deformed partition…
This paper is concerned with the connection between density matrix method, supersymmetric quantum mechanics and Lewis-Riesenfeld invariant theory. It is shown that these three formulations share the common mathematical structure:…
The Dijkgraaf-Vafa approach is used in order to study the Coulomb branch of the Leigh-Strassler massive deformation of N=4 SYM with gauge group U(N). The theory has N=1 SUSY and an N-dimensional Coulomb branch of vacua, which can be…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
We study Penner type matrix models in relation with the Nekrasov partition function of four dimensional \mathcal{N}=2, SU(2) supersymmetric gauge theories with N_F=2,3 and 4. By evaluating the resolvent using the loop equation for general…
We classify all possible four-dimensional N=2 supersymmetric UV-complete gauge theories composed of semi-simple gauge groups and hypermultiplets. We also give appropriate references for all theories with known Seiberg-Witten solutions.
We show that a suitable rescaling of the matrix model coupling constant makes manifest the duality group of the N=2 SYM theory with gauge group SU(2). This is done by first identifying the possible modifications of the SYM moduli preserving…
We use the matrix model to describe the N=2 SO(N)/Sp(N) supersymmetric gauge theories with massive hypermultiplets in the fundamental representation. By taking the tree level superpotential perturbation made of a polynomial of a scalar…
As regular conformal blocks describe the N=2 superconformal gauge theories in four dimensions, irregular conformal blocks are expected to reproduce the instanton partition functions of the Argyres-Douglas theories. In this paper, we…
In this note, we give a method to derive the Seiberg duality by the matrix model. The key fact we used is that the effective actions given by matrix model method should be identical for both electric and magnetic theories. We demonstrate…
We consider the ${\cal N}=4$ Liouville theory by varying the linear dilaton coupling constant $\cal{Q}$. It is known that at two different values of coupling constant ${\cal Q}=\sqrt{{2\over N}},-(N-1)\sqrt{{2\over N}}$ system exhibits two…
The Penner type beta-ensemble for Omega-deformed N=2 SU(2) gauge theory with two massless flavors arising as a limiting case from the AGT conjecture is considered. The partition function can be calculated perturbatively in a saddle-point…
We construct a large-N twisted reduced model of the four-dimensional super Yang-Mills theory coupled to one adjoint matter. We first consider a non-commutative version of the four-dimensional superspace, and then give the mapping rule…
Noncommutative gauge theories defined via Seiberg-Witten map have desirable properties that theories defined directly in terms of noncommutative fields lack, covariance and unrestricted choice of gauge group and charge being among them, but…
We consider how gauge theories can be described by matrix models. Conventional matrix regularization is defined for scalar functions and is not applicable to gauge fields, which are connections of fiber bundles. We clarify how the degrees…
We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N=2 gauge theories. Our construction naturally involves four-dimensional theories with…
We investigate supersymmetric QCD with N_c+1 flavors using an extension of the recently proposed relation between gauge theories and matrix models. The impressive agreement between the two sides provides a beautiful confirmation of the…
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of…