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 R-3 x S-1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U(1) gauge fields A mu(x) which depend on all four spacetime coordinates (including the coordinate x(4) is an element of S-1 of the compact dimension) and have vanishing components A(4)(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. (c) 2017 The Author(s). Published by Elsevier B.V.