Virial expansion of the non-linear sigma model in the strong coupling limit

TL;DR

This paper develops a perturbative approach to analyze the supersymmetric non-linear sigma model in the strong coupling limit, revealing its equivalence to random matrix ensembles and providing explicit calculations of eigenfunction moments and correlations.

Contribution

The paper introduces a novel perturbative method for the non-linear sigma model in strong coupling, establishing its equivalence to random matrix theory across all orders.

Findings

Explicit expressions for eigenfunction moments and two-level correlation functions.

Demonstration of the equivalence between sigma models and random matrix ensembles.

Generalization of the mapping to all orders of perturbation.

Abstract

We develop a perturbative approach to study the supersymmetric non-linear sigma model characterized by a generic coupling matrix in the strong coupling limit. The method allows us to calculate explicitly the moments of the eigenfunctions and the two-level correlation function in the lowest order of the perturbative expansion. We find that the obtained expressions are equivalent to the results derived before for the corresponding random matrix ensembles. Such an equivalence is elucidated and generalized to all orders of the perturbative expansion by mapping the sigma model onto the field theory describing the almost diagonal random matrices.