Induced Lorentz-violating terms at finite temperature

We study the radiatively induced Lorentz-violating terms at finite temperature, namely, the higher-derivative term and the Chern-Simons term. These terms are induced by integrating out the fermions coupled to the coefficient $g^{\kappa\mu\nu}$. The calculation of the resulting expressions is performed by using the derivative expansion and the Matsubara formalism. The Chern-Simons terms is nonzero only at finite temperature, whereas the higher-derivative term is finite at zero temperature, however, it goes to zero as the temperature grows to infinity. We also obtain a higher-derivative Chern-Simons term, nevertheless, it vanishes asymptotically.Comment: 12 pages, 4 figures, revtex4; v2: EPL versio

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

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, $(k_{AF})_0\to0$ 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.Comment: 13 pages, accepted for publication in Europhys. Let

Nonanalyticity of the induced Carroll-Field-Jackiw term at finite temperature

In this paper, we discuss the behavior of the Carroll-Field-Jackiw (CFJ) coefficient $k^{\mu}$ arising due to integration over massive fermions, and the modification suffered by its topological structure in the finite temperature case. Our study is based on the imaginary time formalism and summation over the Matsubara frequencies. We demonstrate that the self-energy of photon is non-analytic for the small $k^{\mu}$ limit, i.e., the static limit $(k_0=0,\vec k\rightarrow 0)$ and the long wavelength limit $(k_0\rightarrow 0,\vec k= 0)$ do not commute, while the tensorial structure of the CFJ term holds in both limits.Comment: 12 pages, 1 figur

On the perturbative generation of the higher-derivative Lorentz-breaking terms

In this paper, we describe the perturbative generation of the higher-derivative Lorentz-breaking terms for the gauge field, that is, the Myers-Pospelov term and the higher-derivative Carroll-Field-Jackiw term. These terms are explicitly calculated in the one-loop approximation and shown to be finite and ambiguous.Comment: 12 pages, version accepted to PR