Abstract
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.
Highlights
It has been shown [1] that chiral gauge theories over a manifold with an appropriate nontrivial topology necessarily have an anomalous violation of Lorentz and CPT invariance
The existence of the CPT anomaly for four-dimensional gauge chiral theories over the spacetime manifold M = R3 × S1 was established in Refs. [1,3] for a special class of background gauge fields, namely gauge-field configurations which are independent of the compact coordinate x4 ∈ S1 and have a vanishing component A4
For the appropriate setup of the physical system (Sec. 2), we have established perturbatively (Sec. 3) the existence of a CPT anomaly for a background gauge field Aμ which depends on the compactified x4 coordinate and has a vanishing component A4
Summary
It has been shown [1] that chiral gauge theories over a manifold with an appropriate nontrivial topology necessarily have an anomalous violation of Lorentz and CPT invariance. The existence of the CPT anomaly for four-dimensional gauge chiral theories over the spacetime manifold M = R3 × S1 was established in Refs. The question arises how the anomaly manifests itself for more general gauge-field configurations which have a nontrivial dependence on the compact x4 coordinate It will be shown, in the present article, that the anomaly manifests itself by a local Chern– Simons-like term in the effective gauge-field action and this term is known to violate Lorentz and CPT invariance [5,6,7]. This effective action is perturbatively expanded and rendered finite with an extended version of the generalized Pauli–Villars regularization. A first impression can be obtained from Secs. 2, 3.3, and 6
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