Related papers: Two-matrix model with semiclassical potentials and…
The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…
In this work we obtain the planar free energy for the Hermitian one-matrix model with various choices of the potential. We accomplish this by applying an approach that bypasses the usual diagonalization of the matrices and the introduction…
We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the tau-function of the dispersionless two--dimensional Toda…
We discuss various aspects of most general multisupport solutions to matrix models in the presence of hard walls, i.e., in the case where the eigenvalue support is confined to subdomains of the real axis. The structure of the solution at…
In this paper we complement our recent result on the explicit formula for the planar limit of the free energy of the two-matrix model by computing the second and third order observables of the model in terms of canonical structures of the…
We derive the discrete linear systems associated to multi--matrix models, the corresponding discrete hierarchies and the appropriate coupling conditions. We also obtain the $W_{1+\infty}$ constraints on the partition function. We then apply…
The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for…
We discuss the relation between matrix models and the Seiberg--Witten type (SW) theories, recently proposed by Dijkgraaf and Vafa. In particular, we prove that the partition function of the Hermitean one-matrix model in the planar (large…
The 2-matrix models can be defined in a setting more general than polynomial potentials, namely, the semiclassical matrix model. In this case, the potentials are such that their derivatives are rational functions, and the integration paths…
We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new…
We study the hermitean and normal two matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex…
We study the full set of planar Green's functions for a two-matrix model using the language of functions of non-commuting variables. Both the standard Schwinger-Dyson equations and equations determining connected Green's functions can be…
We compute the planar limit of both the free energy and the expectation value of the $1/2$ BPS Wilson loop for four dimensional ${\cal N}=2$ superconformal quiver theories, with a product of SU($N$)s as gauge group and bi-fundamental…
We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of ${\cal N}=2$ SQCD on $S^4$, to all orders in the 't Hooft coupling. In order to do so, we first obtain a combinatorial expression for the…
Recently, a two-matrix-model with a new type of interaction [1] has been introduced and analyzed using bi-orthogonal polynomial techniques. Here we present the complete 1/N^2 expansion for the formal version of this model, following the…
We calculate the energy and wave functions of two particles confined to two spatial dimensions interacting via arbitrary anisotropic potentials with negative or zero net volume. The general rigorous analytic expressions are given in the…
We extend the notion of some energy-type expressions based on two sets, developed in the abstract potential theory. We also give the discretized version of the quantities defined, similar to Chebyshev constant. This extension allows to…
For a three-dimensional higher-derivative scalar superfield model, and a four-dimensional higher-derivative chiral superfield model, where which the higher-derivative operators are described by polynomials of arbitrary degrees, we…
We compute the planar limit, as all-order power series in the 't Hooft coupling, of various integrated 4-point functions of chiral primary operators of ${\cal N}=4$ SU(N) super Yang-Mills, and of moment map operators of ${\cal N}=2$ SU(N)…
We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models.…