Soliton metrics for two-loop renormalization group flow on 3D unimodular Lie groups

TL;DR

This paper investigates the two-loop renormalization group flow on 3D unimodular Lie groups, identifying various steady solitons, some related to Ricci flow and others novel, expanding understanding of geometric flows.

Contribution

It introduces a detailed analysis of solitons for the two-loop RG flow on 3D unimodular Lie groups, revealing new steady solutions beyond Ricci flow connections.

Findings

Identification of multiple steady solitons for the two-loop RG flow.

Some solitons originate from symmetric metrics related to Ricci flow.

Discovery of solitons not evidently connected to Ricci flow.

Abstract

The two-loop renormalization group flow is studied via the induced bracket flow on 3D unimodular Lie groups. A number of steady solitons are found. Some of these steady solitons come from maximally symmetric metrics that are steady, shrinking, or expanding solitons under Ricci flow, while others are not obviously related to Ricci flow solitons.