A solution of the Gross-Witten matrix model by nonlinear random processes

TL;DR

This paper demonstrates a stochastic approach to solving Schwinger-Dyson equations in the large-N Gross-Witten matrix model, effectively handling strong and weak coupling regimes through variable transformations and new action formulations.

Contribution

It introduces a novel stochastic method for solving Schwinger-Dyson equations in matrix models, adaptable to different coupling regimes and potentially extendable to other large-N field theories.

Findings

Effective solution in strong-coupling limit

Variable change enables weak-coupling analysis

Handles infinite higher-order interactions efficiently

Abstract

We illustrate the stochastic method for solving the Schwinger-Dyson equations in large-N quantum field theories described in ArXiv:1009.4033 on the example of the Gross-Witten unitary matrix model. In the strong-coupling limit, this method can be applied directly, while in the weak-coupling limit we change the variables from compact to noncompact ones in order to cast the Schwinger-Dyson equations in the stochastic form. This leads to a new action with an infinite number of higher-order interaction terms. Nevertheless, such an action can be efficiently handled. This suggests the way to apply the method of ArXiv:1009.4033 to field theories with U(N) field variables as well as to effective field theories in the large-N limit.