Related papers: Matrix Models, Quantum Penner Action and Two-Dimen…
We show that the most general two--matrix model with bilinear coupling underlies $c=1$ string theory. More precisely we prove that $W_{1+\infty}$ constraints, a subset of the correlation functions and the integrable hierarchy characterizing…
We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back…
We formulate matrix string models on a class of exact string backgrounds with non constant RR-flux parameterized by a holomorphic prepotential function and with manifest (2,2) supersymmetry. This lifts these string theories to M-theory…
We study the CPT theorem for a two-dimensional conformal field theory on an arbitrary Riemann surface. On the sphere the theorem follows from the assumption that the correlation functions have standard hermiticity properties and are…
A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…
This paper provides the constructive loop vertex expansion for stable matrix models with (single trace) interactions of arbitrarily high even order in the Hermitian and real symmetric cases. It relies on a new and simpler method which can…
We study a hermitian $(n+1)$-matrix model with plaquette interaction, $\sum_{i=1}^n MA_iMA_i$. By means of a conformal transformation we rewrite the model as an $O(n)$ model on a random lattice with a non polynomial potential. This allows…
I study tachyon condensate perturbations to the action of the two dimensional string theory corresponding to the c=1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of…
The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into…
We show that the 2-matrix string model corresponds to a coupled system of $2+1$-dimensional KP and modified KP ($\KPm$) integrable equations subject to a specific ``symmetry'' constraint. The latter together with the Miura-Konopelchenko map…
The correlation spectrum of fully developed one-dimensional mappings are studied near and at a weakly intermittent situation. Using a suitable infinite matrix representation, the eigenvalue equation of the Frobenius-Perron operator is…
We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a…
Two-dimensional sigma models are defined for the new manifestly spacetime supersymmetric description of four-dimensional compactified superstrings. The resulting target-superspace effective action is constrained by the way the spacetime…
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links…
We obtain the topological expansion of the hermitian matrix model using its representation as a CFT on a hyperelliptic Riemann surface. To each branch point of the Riemann surface we associate an operator which represents a twist field…
We formulate and solve a class of two-dimensional matrix gauge models describing ensembles of non-folding surfaces covering an oriented, discretized, two-dimensional manifold. We interpret the models as string theories characterized by a…
We discuss the effective action of tachyon in the two dimensional string theory at tree level. We show that already starting from the cubic terms the action is nonlocal and the usually assumed simplest cubic term does not give the correct…
We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
We continue here to study simple matrix models of quantum mechanical Hamiltonians. The eigenvalues and eigenfunctions were associated energy levels and wave functions. Whereas previously we considered the weak coupling limits of our models,…