Axion-dilaton cosmology, Ricci flows and integrable structures

TL;DR

This paper explores the connection between axion-dilaton cosmology, Ricci flows, and integrable systems by analyzing RG flows in conformal sigma-models, revealing the round sphere as a unique IR fixed point.

Contribution

It demonstrates that RG flows in certain sigma-models are described by integrable Ricci flows, specifically the Halphen system, and identifies the round sphere as the unique IR fixed point at one loop.

Findings

Ricci flow equations correspond to the Halphen system in three-sphere backgrounds.

The round sphere is the only perturbative IR fixed point at one loop.

The study links integrable structures with RG flows in string-inspired models.

Abstract

In this work we study renormalization-group flows by deforming a class of conformal sigma-models. At leading order in $\alpha'$, renormalization-group equations represent a Ricci flow. In the three-sphere background, the latter is described by the Halphen system, which is exactly solvable in terms of modular forms. The round sphere is found to be the unique perturbative infra-red fixed point at one loop order.