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.

Extended version. RevTex, 44 pages

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• Covariant derivative expansion of the heat kernel
• Derivative expansion of the heat kernel in curved space
• Gauge invariant derivative expansion of the effective action at finite temperature and density and the scalar field in 2+1 dimensions
• The method of covariant symbols in curved space-time
• Effective action for QED in 2+1 dimensions at finite temperature
• The induced Chern-Simons term at finite temperature
• Finite Temperature Effective Action in Monopole Background
• Derivative Expansion and the Effective Action for the Abelian Chern-Simons Theory at Higher Orders
• Temperature dependence of the anomalous effective action of fermions in two and four dimensions
• Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry
• Non-static Dimensional Reduction of QED_3 at Finite Temperature
• Induced parity violating thermal effective action for (2+1)-dimensional fermions interacting with a non-Abelian background
• Large Gauge Invariance in NonAbelian Finite Temperature Effective Actions