Two-logarithm matrix model with an external field

TL;DR

This paper studies a specific matrix model with a two-logarithm potential, demonstrating its equivalence to the Kontsevich-Penner model and providing an explicit 1/N-expansion solution.

Contribution

It establishes the equivalence between the two-logarithm matrix model and the Kontsevich-Penner model and constructs its 1/N-expansion solution.

Findings

Proves the model's equivalence using Virasoro constraints

Constructs the 1/N-expansion solution explicitly

Links the model to an exactly solvable Kazakov-Migdal model

Abstract

We investigate the two-logarithm matrix model with the potential $X\Lambda+\alpha\log(1+X)+\beta\log(1-X)$ related to an exactly solvable Kazakov-Migdal model. In the proper normalization, using Virasoro constraints, we prove the equivalence of this model and the Kontsevich-Penner matrix model and construct the 1/N-expansion solution of this model.