Single copy of the Ricci flow

TL;DR

This paper reveals that the single copy of the Ricci flow corresponds to the Yang-Mills flow on the space of connections of a U(1)-bundle, extending the double copy correspondence to non-perturbative regimes.

Contribution

It demonstrates that the Ricci flow's single copy is equivalent to the Yang-Mills flow on U(1) connections, linking geometric evolution to gauge theory dynamics.

Findings

Ricci flow's single copy is Yang-Mills flow on U(1) connections

Extends double copy correspondence to non-perturbative regimes

Provides new insights into geometric and gauge theory relations

Abstract

The perturbative double copy is by now a highly established correspondence between gravity and gauge theories. Non-perturbatively, information ranging from classical solutions to topological quantities on both sides have been related to each other via the double copy correspondence. In this paper, we add another result, where we show that the single copy of the Ricci flow is the Yang-Mills flow on the space of connections of a principal $\text{U}(1)$-bundle.