Renormalization Group and the Ricci flow

TL;DR

This paper explores the relationship between the renormalization group flow in non-linear sigma models and the Ricci flow, offering geometric insights into quantum field theories and potential extensions beyond weak coupling.

Contribution

It provides a geometric perspective linking RG flow and Ricci flow, proposing a way to extend the embedding beyond weak coupling regimes.

Findings

Ricci flow singularities suggest natural extensions of RG flow

Geometric landscape for 2D quantum field theories is proposed

New perspectives on non-linear sigma models are introduced

Abstract

We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests a natural way for extending, beyond the weak coupling regime, the embedding of the Ricci flow into the renormalization group flow.