Parity breaking in 2+1 dimensions and finite temperature

Abstract

An expansion in the number of spatial covariant derivatives is carried out to compute the $\zeta$-function regularized effective action of 2+1-dimensional fermions at finite temperature in an arbitrary non-Abelian background. The real and imaginary parts of the Euclidean effective action are computed up to terms which are ultraviolet finite. The expansion used preserves gauge and parity symmetries and the correct multivaluation under large gauge transformations as well as the correct parity anomaly are reproduced. The result is shown to correctly reproduce known limiting cases, such as massless fermions, zero temperature, and weak fields as well as exact results for some Abelian configurations. Its connection with chiral symmetry is discussed.