Induced Parity Breaking Term in Arbitrary Odd Dimensions at Finite Temperature

Abstract

We calculate the exact parity odd part of the effective action (${\Gamma }_{odd}^{2d+1}$) for massive Dirac fermions in 2d+1 dimensions at finite temperature, for a certain class of gauge field configurations. We consider first Abelian external gauge fields, and then we deal with the case of a non-Abelian gauge group containing an Abelian U(1) subgroup. For both cases, it is possible to show that the result depends on topological invariants of the gauge field configurations, and that the gauge transformation properties of ${\Gamma }_{odd}^{2d+1}$ depend only on those invariants and on the winding number of the gauge transformation.

10 pages, revtex, no figures

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• The fermion-boson map for large d
• Momentum-Dependent Mass and AC Hall Conductivity of Quantum Anomalous Hall Insulators and Their Relation to the Parity Anomaly
• Derivative Expansion and the Effective Action for the Abelian Chern-Simons Theory at Higher Orders
• Parity Violating Bosonic Loops at Finite Temperature
• 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