The sausage sigma model revisited

TL;DR

This paper investigates the stability of Fateev's sausage sigma models under Ricci flow, revealing that the 3D model is unstable while the 2D model is stable, and suggests potential new solutions related to RG flow deformations.

Contribution

It analyzes the stability of sausage sigma models using Ricci flow mathematics and proposes the existence of new RG flow solutions as perturbations of the sausage models.

Findings

3D sausage is unstable under RG flow.

2D sausage appears stable and approaches the sphere.

A class of decoupled perturbations suggests new RG flow solutions.

Abstract

Fateev's sausage sigma models in two and three dimensions are known to be integrable. We study their stability under RG flow in the target space by using results from the mathematics of Ricci flow. We show that the three dimensional sausage is unstable, whereas the two dimensional sausage appears to be stable at least at leading order as it approaches the sphere. We speculate that the stability results obtained are linked to the classification of ancient solutions to Ricci flow (i.e., sigma models which are nonperturbative in the IR) in two and three dimensions. We also describe a class of perturbations of the three dimensional sausage (with the same continuous symmetries) which remarkably decouple. This indicates that there could be a new solution to RG flow which is described at least perturbatively as a deformation of the sausage.