Induced Chern-Simons term by dimensional reduction

Abstract

We derive an induced Abelian Chern-Simons (CS) term in 2+1 dimensions, by dimensional reduction from the finite-temperature theory of a Dirac field with both vector and axial-vector couplings to two Abelian gauge fields, in 3+1 dimensions. In our construction, the CS term emerges for the lowest Matsubara mode of the vector Abelian field, by integrating the fermionic field, under the assumption that the axial-vector field is in a "vacuum"configuration. This configuration is characterized by a single number, which in turn determines the coefficient of the induced CS term for the Abelian vector field.