The Variational Problem and Background Field in the Renormalization Group Method for Non-Linear Sigma Models

TL;DR

This paper adapts the variational problem from Yang-Mills theories to Non-Linear Sigma Models in two dimensions, providing a minimal configuration that acts as a classical background field in renormalization group analysis.

Contribution

It introduces a novel adaptation of the variational problem for Non-Linear Sigma Models within the renormalization group framework, extending previous methods from Yang-Mills theories.

Findings

Derived a minimal configuration serving as a background field.

Extended the variational problem to 2D Non-Linear Sigma Models.

Facilitated renormalization group analysis for these models.

Abstract

We study the variational problem as described by Balaban in his renormalization group method for Yang-Mills theories in $d= 3, 4$ and adapt it to a class of Non-Linear Sigma Models in $d=2$. The result of the variational problem is a minimal configuration which can serve as a classical background field in the renormalization group analysis.