Two-Matrix model with ABAB interaction

TL;DR

This paper exactly solves a new two-matrix model with ABAB interactions using character expansions, revealing a phase transition to a conformal field theory coupled with 2D quantum gravity.

Contribution

It introduces an exact solution for a novel two-matrix model with ABAB interactions in the large N limit, connecting it to the 8-vertex model and elliptic functions.

Findings

Identifies a phase transition point with a c=1 conformal field theory

Maps the matrix model to a special case of the 8-vertex model

Uses elliptic functions for parametrization of the solution

Abstract

Using recently developed methods of character expansions we solve exactly in the large N limit a new two-matrix model of hermitean matrices A and B with the action S={1\over 2}(\tr A^2+\tr B^2)-{\alpha\over 4}(\tr A^4+\tr B^4) -{\beta\over 2} \tr(AB)^2. This model can be mapped onto a special case of the 8-vertex model on dynamical planar graphs. The solution is parametrized in terms of elliptic functions. A phase transition is found: the critical point is a conformal field theory with central charge c=1 coupled to 2D quantum gravity.