Fixed Points of Nonlinear Sigma Models in d>2

TL;DR

This paper investigates the renormalization group flow of nonlinear sigma models in dimensions greater than two, revealing a nontrivial fixed point that could serve as an ultraviolet limit despite nonrenormalizability.

Contribution

It provides a detailed analysis of the RG flow using Wilsonian methods and identifies a nontrivial fixed point in higher dimensions, extending understanding of sigma models.

Findings

Ricci flow at one loop for the RG

Existence of a nontrivial fixed point for d>2

Potential for defining an ultraviolet limit

Abstract

Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely fix the internal metric, we compute the beta function of the single remaining coupling, without any further approximation. For $d>2$ and positive curvature, there is a nontrivial fixed point, which could be used to define an ultraviolet limit, in spite of the perturbative nonrenormalizability of the theory. Potential applications are briefly mentioned.