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

2015/05/29 by J. F. Assunção, Assuncao, J. F., T. Mariz +1
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.1505.08156

openalex publication_date 2015/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)_μ=-(e²)/(4π²) b_μ. 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)_μ, in which at high temperature, (k_AF)₀→0 and (k_AF)_i→-(e²)/(4π²)b_i. In the context of Weyl semimetals, these results are in accordance with the fact that the chiral magnetic current j^α=(k_AF)₀ε^0αλρ∂_λA_ρ vanishes at high temperature, whereas the anomalous Hall current j^α=(k_AF)_iε^iαλρ∂_λA_ρ remains unaffected by the finite temperature.

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