Some Applications of Ricci Flow in Physics
High Energy Physics - Theory
2009-11-13 v3 General Relativity and Quantum Cosmology
Differential Geometry
Abstract
I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci soliton and recall how a soliton was used to discuss the RG flow of mass in 2-dimensions. I then present recent results obtained with Oliynyk on the flow of mass in higher dimensions. The final section discusses one way in which Ricci flow may arise in general relativity, particularly for static metrics.
Cite
@article{arxiv.0708.2144,
title = {Some Applications of Ricci Flow in Physics},
author = {E. Woolgar},
journal= {arXiv preprint arXiv:0708.2144},
year = {2009}
}
Comments
Minor corrections in Sections IV and VI. Invited talk at Theory Canada III meeting, June 2007; submitted to Proceedings. Dedicated to Rafael D Sorkin on the occasion of his 60th birthday