Abstract
If there exists Lorentz and CPT violation in nature, then it is crucial to discover and understand the underlying mechanism. In this contribution, we discuss one such mechanism which relies on four-dimensional chiral gauge theories defined over a spacetime manifold with topology ℛ3 × S1 and periodic spin structure for the compact dimension. It can be shown that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. For arbitrary Abelian U(1) gauge fields with trivial holonomies in the compact direction, this anomalous Lorentz and CPT violation has recently been established perturbatively with a Pauli–Villars-type regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.
Highlights
Experiment has shown the violation of P, C, CP, and T, but not of CPT
The following question arises: can CPT invariance be violated at all in a physical theory and, if so, is it in the real world? It was widely believed that only quantum-gravity or superstring effects could give CPT violation
We focus on the basic mechanism of the CPT anomaly and skip possible applications
Summary
Experiment has shown the violation of P, C, CP, and T, but not of CPT. there is the well-known CPT “theorem” (Luders, 1954–57; Pauli, 1955; Bell, 1955; Jost, 1957), which states that any local relativistic quantum field theory is invariant under the combined operation (in whichever order) of charge conjugation (C), parity reflection (P), and time reversal (T). A different result has been obtained several years ago: for certain spacetime topologies and classes of chiral gauge theories, CPT invariance is broken anomalously, that is, by quantum effects. 2. Heuristics The CPT anomaly of a chiral gauge theory defined over the four-dimensional manifold M = R3 × S1, with trivial vierbeins eaμ(x) = δμa and appropriate background gauge fields, arises in four steps:. Our anomalous action term (6) holds, in four spacetime dimensions: the integration is over four spacetime coordinates and the gauge fields Aμ have a dependence on x3. The local term (6) is Lorentz-noninvariant, because of the explicit spacetime index “3” entering the Levi–Civita symbol, and is CPT-odd, because of the odd number (namely, three) of spacetime indices for the gauge-field terms in the large brackets. Recall that the standard Yang–Mills action density term tr Aμν (x) Aμν (x) is Lorentz-invariant and CPT-even [17]
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