The asymmetric ABAB matrix model

TL;DR

This paper extends the solution of a two-matrix model with asymmetric quartic interactions in the large N limit, potentially aiding the study of 3D Lorentzian gravity.

Contribution

It generalizes the existing symmetric matrix model solution to asymmetric cases, providing a new solvable model relevant for quantum gravity.

Findings

The asymmetric ABAB matrix model can be solved in the large N limit.

The solution generalizes Kazakov and Zinn-Justin's symmetric case.

Potential applications to 3D Lorentzian gravity are identified.

Abstract

In this letter, it is pointed out that the two matrix model defined by the action S=(1/2)(tr A^2+tr B^2)-(alpha_A/4) tr A^4-(alpha_B/4) tr B^4-(beta/2) tr(AB)^2 can be solved in the large N limit using a generalization of the solution of Kazakov and Zinn-Justin (who considered the symmetric case alpha_A=alpha_B). This model could have useful applications to 3D Lorentzian gravity.