Wilsonian renormalization group approach to the lower dimensional nonlinear sigma models

TL;DR

This paper explores the renormalization and phase structure of three-dimensional nonlinear sigma models using Wilsonian renormalization group and large-N expansion, identifying fixed points and conformal field theories.

Contribution

It demonstrates the existence of nontrivial UV fixed points in certain models and constructs conformal field theories at these points using nonperturbative methods.

Findings

Some models are renormalizable with nontrivial UV fixed points.

$CP^{N-1}$ and $Q^{N-2}$ models exhibit multiple phases.

Conformal field theories are constructed at fixed points.

Abstract

In this paper, we study three dimensional NL$\sigma$Ms within two kind of nonperturbative methods; WRG and large-N expansion. First, we investigate the renormalizability of some NL$\sigma$Ms using WRG equation. We find that some models have a nontrivial UV fixed point and are renormalizable within nonperturbative method. Second, we study the phase structure of $CP^{N-1}$ and $Q^{N-2}$ models using large-N expansion. These two models have two and three phases respectively. At last, we construct the conformal field theories at the fixed point of the nonperturbative WRG $\beta$ function. This is the review of recently works and is based on the talk of the conference by EI.