Driving Operators Relevant: A Feature of Chern-Simons Interaction

TL;DR

This paper investigates how Chern-Simons interactions influence the relevance of certain operators in fermion and boson models, identifying critical couplings where phase transitions occur due to operators becoming marginal.

Contribution

It computes anomalous dimensions of composite operators in Chern-Simons models and identifies critical couplings for phase transitions where operators change relevance.

Findings

Critical Chern-Simons couplings for phase transitions.

Operators become marginal at specific couplings.

Phenomenon observed in both fermion and boson models, including $1/N$ expansion.

Abstract

By computing anomalous dimensions of gauge invariant composite operators $(\bar\psi\psi)^n$ and $(\phi^*\phi)^n$ in Chern-Simons fermion and boson models, we address that Chern-Simons interactions make these operators more relevant or less irrelevant in the low energy region. We obtain a critical Chern-Simons fermion coupling, ${1\over \kappa_c^2} = {6\over 19}$, for a phase transition at which the leading irrelevant four-fermion operator $(\bar\psi\psi)^2$ becomes marginal, and a critical Chern-Simons boson coupling, ${1\over \kappa_c^2} = {6\over 34}$, for a similar phase transition for the leading irrelevant operator $(\phi^*\phi)^4$. We see this phenomenon also in the $1/N$ expansion.