Instantons in $\sigma$ model and tau functions

TL;DR

This paper demonstrates how multiple integrals, including instanton contributions in the 2D O(3) sigma model, can be interpreted as tau functions of integrable hierarchies, linking quantum field theory and integrable systems.

Contribution

It introduces a novel perspective by representing instanton effects in the sigma model as tau functions, bridging quantum field theory with integrable hierarchies.

Findings

Multiple integrals can be viewed as tau functions.

Instanton contributions are expressed through integrable hierarchies.

Establishes a connection between sigma models and integrable systems.

Abstract

We show that a number of multiple integrals may viewed as tau functions of various integrable hierarchies. The instanton contributions in the two-dimensional O(3)$\ \sigma $ model is an example of such an approach.