Veranstaltung

Vortrag
A gradient flow for non-linear sigma models: some applications of Hamilton-Perelman theory
Eric Woolgar
22.11.2006, 13:00 Uhr

Renormalization group flow for nonlinear sigma models can be approximated by Ricci flow when the B-field and stringy corrections beyond first order are unimportant. Thus, results from the study of Ricci flow should have applications in the physics of the sigma model. I will discuss some of these applications. In particular, Perelman has shown that Ricci flow is gradient with respect to a positive-definite metric on the space of Riemannian metrics if the coordinate gauge is chosen wisely. I will describe how this generalizes to give a gradient flow and monotonicity formula on the space of coupling constants of the sigma model with B-field, to first order in the string scale and modulo a suitable gauge choice. I will also describe recent results on the spherically symmetric Ricci flow that indicate the behaviour of mass under RG flow on asymptotically flat manifolds. Time permitting, I will put forward some open problems. This talk is based on joint papers with my collaborators Todd Oliynyk and Suneeta Vardarajan.

Notes (PDF): http://www.aei.mpg.de/~olito/WS/Talks/Woolgar.pdf