Non-analyticity of the induced Carroll-Field-Jackiw term at finite temperature

Abstract

In this paper, we discuss the behavior of the Carroll-Field-Jackiw (CFJ) coefficient k µ 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 µ limit, i.e., the static limit (k 0 = 0, k → 0) and the long wavelength limit (k 0 → 0, k = 0) do not commute, while the tensorial structure of the CFJ term holds in both limits. * Electronic address: jfassuncao,tmariz@fis.ufal.br † Electronic address: petrov@fisica.ufpb.br

Nonanalyticity of the nonabelian five-dimensional Chern-Simons term

“…The result obtained in equation ( 31) correspond to that one in equation (25), showing that the derivative expansion method is consistent only to obtain the static limit. This fact is also found in three- [12,23] and four-dimensional [11,24] theories.…”

“…Thus, as due to the choice of a specific frame by the thermal bath the radiative corrections, in general, has different dependencies of k 0 and k, the two conditions (k 0 = 0, k → 0) and (k 0 → 0, k = 0) do not commute. In fact, this has been shown in the case of Lorentz-violating QED [11], three-dimensional QED [12], hot QCD [13][14][15], self-interacting scalars [16], and Maxwell-Chern-Simons-Higgs model [17]. The first condition (k 0 = 0, k → 0) is sometimes referred as the "static" limit, while the other condition (k 0 → 0, k = 0) is the "long wavelength" limit.…”

“…where α is a constant. These expressions (10), (11), and ( 12) are presented in Fig. 1, respectively.…”

Effects of Lorentz violation in the Bose-Einstein condensation

“…The finite temperature effects in the context of Lorentz symmetry violation have been extensively studied in the last years, specially in the context of radiative corrections [9][10][11], tree level scatterings [12][13][14][15], massless QED [16], ambiguities in the Chern-Simons induction and non-analiticity [17][18][19]. In this paper we are interested in the influence of the Lorentzviolating extension of the scalar sector [7] in the finite temperature regime and particularly in the Bose-Einstein condensation.…”