Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach

TL;DR

This paper applies the functional renormalization group to non-linear sigma models on constant curvature manifolds, focusing on background field invariance and curvature expansion to analyze their renormalization behavior.

Contribution

It introduces a curvature-based expansion approach within the functional renormalization group framework for non-linear sigma models, clarifying previous methods.

Findings

Flow equations are closed to first order in curvature.

Reparametrization invariance is maintained via Ward identities.

Provides new insights into background field method applications.

Abstract

We study non-linear sigma models on target manifolds with constant (positive or negative) curvature using the functional renormalization group and the background field method. We pay particular attention to the splitting Ward identities associated to the invariance under reparametrization of the background field. Implementing these Ward identities imposes to use the curvature as a formal expansion parameter, which allows us to close the flow equation of the (scale-dependent) effective action consistently to first order in the curvature. We shed new light on previous work using the background field method.