Related papers: On Geometry and Matrix Models
Unitary 1-matrix models are shown to be exactly equivalent to hermitian 1-matrix models coupled to 2N vectors with appropriate potentials, to all orders in the 1/N expansion. This fact allows us to use all the techniques developed and…
We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric…
We solve $\mathcal{N}=1$ supersymmetric $A_{2}$ type $U(N)\times U(N)$ matrix models obtained by deforming $\mathcal{N}=2$ with symmetric tree level superpotentials of any degree exactly in the planar limit. These theories can be…
We provide a proof of the equivalence of N=1 dynamics obtained by deforming N=2 supersymmetric gauge theories by addition of certain superpotential terms, with that of type IIB superstring on Calabi-Yau threefold geometries with fluxes. In…
Dijkgraaf and Vafa have conjectured that the effective superpotentials for N=1 four-dimensional supersymmetric gauge theories can be given by the planar diagrams of matrix models. We examine some special models with cubic and quartic tree…
A popular way to study N=1 supersymmetric gauge theories is to realize them geometrically in string theory, as suspended brane constructions, D-branes wrapping cycles in Calabi-Yau manifolds, orbifolds, and otherwise. Among the applications…
We compute the prepotential of N=2 supersymmetric gauge theories in four dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as a function of Kahler and complex moduli of T^2. We use three different…
We extend the results of Cachazo, Seiberg and Witten to N=1 supersymmetric gauge theories with gauge groups SO(2N), SO(2N+1) and Sp(2N). By taking the superpotential which is an arbitrary polynomial of adjoint matter \Phi as a small…
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…
We argue that for a large class of N=1 supersymmetric gauge theories the effective superpotential as a function of the glueball chiral superfield is exactly given by a summation of planar diagrams of the same gauge theory. This perturbative…
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 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…
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 construct N=1 supersymmetric theories on worldvolumes of D5 branes wrapped around 2-cycles of threefolds which are A-D-E fibrations over a plane. We propose large N duals as geometric transitions involving blowdowns of two cycles and…
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N} = 1$…
We show how the Dijkgraaf-Vafa matrix model proposal can be extended to describe five-dimensional gauge theories compactified on a circle to four dimensions. This involves solving a certain quantum mechanical matrix model. We do this for…
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating…
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 study the superpotentials, quantum parameter space and phase transitions that arise in the study of large N dualities between $\mathcal{N}=1$ SUSY U(N) gauge theories and string models on local Calabi-Yau manifolds. The main tool of our…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…