Stability of the (two-loop) Renormalization Group Flow for Nonlinear Sigma Models

TL;DR

This paper proves the stability of certain geometric spaces, like the torus and hyperbolic space, under the two-loop renormalization group flow for nonlinear sigma models using maximal regularity techniques.

Contribution

It extends stability results to the two-loop renormalization group flow for nonlinear sigma models, employing methods similar to Ricci flow stability proofs.

Findings

Stability of the torus under two-loop RG flow.

Stability of hyperbolic space with rescaling.

Application of maximal regularity theory to RG flow.

Abstract

We prove the stability of the torus, and with suitable rescaling, hyperbolic space under the (two-loop) renormalization group flow for the nonlinear sigma model. To prove stability we use similar techniques to \cite{GIK02}, where the stability of the torus under Ricci flow was first established. The main technical tool is maximal regularity theory.