Some Applications of Ricci Flow in Physics

Details Some Applications of Ricci Flow in Physics Some Applications of Ricci Flow in Physics

2007-08-16

arxiv.org/abs/0708.2144v3

Can.J.Phys.86:645,2008

Physics

High Energy Physics

High Energy Physics - Theory

Minor corrections in Sections IV and VI. Invited talk at Theory Canada III meeting, June 2007; submitted to Proceedings. Dedic

Scientific paper

10.1139/P07-146

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.

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