Radiatively induced CPT-odd Chern-Simons term in massless QED

Abstract

In this work, we study the radiative generation of the CPT-odd Lorentz-violating Chern-Simons term, arising from massless fermions. For this, we calculate the vacuum polarization tensor using the ’t Hooft-Veltman regularization scheme, in which the result obtained for the coefficient of the Chern-Simons term is . This result leads us precisely to the same conductivity found in Weyl semimetals, i.e., the ’t Hooft-Veltman regularization scheme is the correct one to be used in this context. We also discuss the temperature dependence of , in which at high temperature, and . In the context of Weyl semimetals, these results are in accordance with the fact that the chiral magnetic current vanishes at high temperature, whereas the anomalous Hall current remains unaffected by the finite temperature.