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 $(k_{AF}{)}_{\mu }=-\frac{e^2}{4{\pi }^2}{b}_{\mu }$. 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 $(k_{AF}{)}_{\mu }$, in which at high temperature, $(k_{AF}{)}_0\to 0$ and $(k_{AF}{)}_i\to -\frac{e^2}{4{\pi }^2}{b}_i$. In the context of Weyl semimetals, these results are in accordance with the fact that the chiral magnetic current $j^{\alpha }=(k_{AF}{)}_0{\epsilon }^{0\alpha \lambda \rho }{\partial }_{\lambda }{A}_{\rho }$ vanishes at high temperature, whereas the anomalous Hall current $j^{\alpha }=(k_{AF}{)}_i{\epsilon }^{i\alpha \lambda \rho }{\partial }_{\lambda }{A}_{\rho }$ remains unaffected by the finite temperature.

13 pages, accepted for publication in Europhys. Lett