The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions
High Energy Physics - Theory
2009-05-08 v1 General Relativity and Quantum Cosmology
Differential Geometry
Abstract
We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic.
Cite
@article{arxiv.0904.1241,
title = {The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions},
author = {Todd A. Oliynyk},
journal= {arXiv preprint arXiv:0904.1241},
year = {2009}
}