New Conformal Field Theories with Anomalous Dimensions

TL;DR

This paper discovers new fixed point theories in 2D and 3D non-linear sigma models using Wilsonian RG, revealing connections to known models and identifying marginal deformations with anomalous dimensions.

Contribution

It introduces a class of fixed point theories for 2D and 3D sigma models, including a novel 3D model with a parameter for marginal deformation.

Findings

2D fixed point equivalent to Witten's semi-infinite cigar model

3D fixed point exhibits a marginal deformation parameter

Identification of anomalous dimensions in the new fixed points

Abstract

We find a class of fixed point theory for 2- and 3-dimensional non-linear sigma models using Wilsonian renormalization group (WRG) approach. In 2-dimensional case, the fixed point theory is equivalent to the Witten's semi-infinite cigar model. In 3-dimensional case, the theory has one parameter which describes a marginal deformation from the infrared to ultraviolet fixed points of the $CP^N$ model in the theory spaces.