Phase structure of Abelian Chern-Simons gauge theories

TL;DR

This paper investigates how adding a Chern-Simons term influences the phase structure of Abelian gauge theories, revealing phase transitions and critical exponents that depend on the CS coupling strength.

Contribution

It provides a detailed analysis of the phase behavior in both compact and noncompact Abelian gauge theories with a CS term, including Monte Carlo simulations and universality class identification.

Findings

Compact Maxwell-Chern-Simons theory exhibits a phase transition in the 3dXY universality class at specific CS couplings.

Critical exponents in the noncompact Abelian Higgs model vary continuously with the CS term strength.

Monte Carlo simulations support the analytical predictions and reveal the dependence of phase structure on the CS coupling.

Abstract

We study the effect of a Chern-Simons (CS) term in the phase structure of two different Abelian gauge theories. For the compact Maxwell-Chern-Simons theory, we obtain that for values $g=n/2\pi$ of the CS coupling with $n=\pm 1,\pm 2$, the theory is equivalent to a gas of closed loops with contact interaction, exhibiting a phase transition in the $3dXY$ universality class. We also employ Monte Carlo simulations to study the noncompact U(1) Abelian Higgs model with a CS term. Finite size scaling of the third moment of the action yields critical exponents $\alpha$ and $\nu$ that vary continuously with the strength of the CS term, and a comparison with available analytical results is made.