GAUGE-INVARIANCE AND FINITE-TEMPERATURE EFFECTIVE ACTIONS OF CHERN-SIMONS GAUGE-THEORIES WITH FERMIONS

We discuss the behavior of theories of fermions coupled to Chem-Simons gauge fields with a non-abelian gauge group in three dimensions and a t finite temperature, Using non-perturbative arguments and gauge invar iance, and in contradiction with perturbative results, we show that th e coefficient of the Chem-Simons term of the effective actions for the gauge fields at finite temperature can be at most an integer function of the temperature. This is in a sense a generalized no-renormalizati on theorem. We also discuss the case of abelian theories and give indi cations that a similar condition should hold there too. We discuss con sequences of our results to the thermodynamics of anyon superfluids an d fractional quantum Hall systems.