Anomalous Lorentz and CPT violation from a local Chern-Simons-like term in the effective gauge-field action

We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U(1) gauge fields Aμ(x) which depend on all four spacetime coordinates (including the coordinate x4∈S1 of the compact dimension) and have vanishing components A4(x) (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli-Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.