Gauge Invariance and Finite Temperature Effective Actions of Chern-Simons Gauge Theories with Fermions

TL;DR

This paper demonstrates that the Chern-Simons term coefficient in fermionic gauge theories at finite temperature is quantized as an integer function, revealing a generalized no-renormalization theorem with implications for condensed matter systems.

Contribution

It establishes a non-perturbative, gauge-invariant proof that the Chern-Simons coefficient is at most an integer function of temperature, extending the understanding of topological terms at finite temperature.

Findings

Chern-Simons coefficient is at most an integer function of temperature.

Contradicts previous perturbative results with non-perturbative arguments.

Implications for thermodynamics of anyon superfluids and fractional quantum Hall systems.

Abstract

We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction with perturbative results, we show that the coefficient of the Chern-Simons term of the effective actions for the gauge fields at finite temperature can be {\it at most} an integer function of the temperature. This is in a sense a generalized no-renormalization theorem. We also discuss the case of abelian theories and give indications that a similar condition should hold there too. We discuss consequences of our results to the thermodynamics of anyon superfluids and fractional quantum Hall systems.