The structure of radiatively induced Lorentz and CPT violation in QED at finite temperature

TL;DR

This paper investigates the finite-temperature behavior of Lorentz- and CPT-violating terms in QED, revealing a temperature-dependent Chern-Simons-like structure that respects Ward identities and vanishes at zero temperature.

Contribution

It demonstrates that a Lorentz- and CPT-violating term in QED at finite temperature has a specific temperature dependence and is unambiguously determined up to a temperature-independent constant.

Findings

The Lorentz- and CPT-violating term does not depend on the temporal component of the fixed vector.

The coefficient of the term vanishes at zero temperature.

The term's form is a Chern-Simons-like structure that respects Ward identities.

Abstract

We obtain the induced Lorentz- and CPT-violating term in QED at finite temperature using imaginary-time formalism and dimensional regularization. Its form resembles a Chern-Simons-like structure, but, unexpectedly, it does not depend on the temporal component of the fixed $b_\mu$ constant vector that is coupled to the axial current. Nevertheless Ward identities are respected and its coefficient vanishes at T=0, consistently with previous computations with the same regularization procedure, and it is a non-trivial function of temperature. We argue that at finite $T$ a Chern-Simons-like Lorentz- and CPT-violating term is generically present, the value of its coefficient being unambiguously determined up to a $T-$independent constant, related to the zero-temperature renormalization conditions.