%0 Journal Article
%T The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions
%A Todd A. Oliynyk
%J Mathematics
%D 2009
%I arXiv
%R 10.1088/0264-9381/26/10/105020
%X 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.
%U http://arxiv.org/abs/0904.1241v1