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We consider four-dimensional chiral gauge theories defined over a spacetimemanifold with topology $\mathbb{R}^3 \times S^1$ and periodic boundaryconditions over the compact dimension. The effective gauge-field action iscalculated for Abelian $U(1)$ gauge fields $A_{\mu}(x)$ which depend on allfour spacetime coordinates (including the coordinate $x^{4}\in S^1$ of thecompact dimension) and have vanishing components $A_{4}(x)$ (implying trivialholonomies in the 4-direction). Our calculation shows that the effectivegauge-field action contains a local Chern-Simons-like term which violatesLorentz and CPT invariance. This result is established perturbatively with ageneralized Pauli-Villars regularization and nonperturbatively with a latticeregularization based on Ginsparg-Wilson fermions.

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