BGWM as Second Constituent of Complex Matrix Model

TL;DR

This paper identifies the Brezin-Gross-Witten (BGW) partition function as a fundamental component in the decomposition of the complex matrix model, expanding the understanding of matrix model building blocks in theoretical physics.

Contribution

It reveals that the BGW tau-function, alongside the Kontsevich tau-function, is essential for decomposing the complex matrix model, highlighting its role as a basic building block.

Findings

BGW tau-function is a key component in complex matrix model decomposition.

The BGW tau-function can be represented as a generating function of unitary-matrix integrals.

It can also be expressed as a Kontsevich-Penner model with potential 1/X.

Abstract

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less topical complex matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).