Quantum Fluctuations and Geometry: From Graph Counting to Ricci Flow

TL;DR

This paper explores the relationship between quantum field theories, specifically non-linear sigma models, and geometric flows like Ricci flow, highlighting how quantum fluctuations influence geometric evolution.

Contribution

It provides a general discussion on quantum field theories involving maps between Riemannian manifolds and elucidates the connection between renormalization group flow and Ricci flow.

Findings

Connection established between quantum fluctuations and geometric evolution.

Insights into how renormalization group flow relates to Ricci flow.

Potential implications for understanding quantum effects on geometry.

Abstract

We discuss in rather general terms quantum field theories dealing with spaces of maps between Riemannian manifolds. In particular we explore the well--known connection between the renormalization group flow for non--linear sigma models and the Ricci flow.