In this work we investigate the radiatively induced Chern-Simons-like terms in four-dimensions at zero and finite temperature. We use the approach of rationalizing the fermion propagator up to the leading order in the CPT-violating coupling b µ . In this approach, we have shown that although the coefficient of Chern-Simons term can be found unambiguously in different regularization schemes at zero or finite temperature, it remains undetermined. We observe a correspondence among results obtained at finite and zero temperature.

We investigate the radiatively induced Chern-Simons-like term in fourdimensional field theory at finite temperature. The Chern-Simons-like term is temperature dependent and breaks the Lorentz and CPT symmetries. We find that this term remains undetermined although it can be found unambiguously in different regularization schemes at finite temperature.

We verify the consistency of the Gödel-type solutions within the four-dimensional ChernSimons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and discuss the related causality issues. We show that, unlike the general relativity, a vacuum solution is possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for a physically wellmotivated matter.

We consider the metric-affine formulation of bumblebee gravity, derive the field equations, and show that the connection can be written as Levi-Civita of a disformally related metric in which the bumblebee field determines the disformal part. As a consequence, the bumblebee field gets coupled to all the other matter fields present in the theory, potentially leading to nontrivial phenomenological effects. To explore this issue we compute the post-Minkowskian, weak-field limit and study the resulting effective theory. In this scenario, we couple scalar and spinorial matter to the effective metric, and then we explore the physical properties of the VEV of the bumblebee field, focusing mainly on the dispersion relations and the stability of the resulting effective theory.

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In this paper, we describe the quantum electrodynamics added by Lorentz-violating CPTeven terms in the context of the standard model extension. We focus our attention on the fermion sector, represented by the CPT-even symmetric Lorentz-breaking tensor c µν . We adopt a generic form that parametrizes the components of c µν in terms of one four-vector, namely, c µν = u µ u ν − ζ u 2 4 g µν . We then generate perturbatively, up to the third order in this tensor, the aether-like term for the gauge field. Finally, we discuss the renormalization scheme for the gauge propagator, by taking into account c µν traceless (ζ = 1) and, trivially, c µν = u µ u ν (ζ = 0). * Electronic address: r.v.maluf@fisica.ufc.br † Electronic address: jroberto@fisica.ufpb.br ‡ Electronic address: petrov@fisica.ufpb.br § Electronic address: tmariz@fis.ufal.br 1 arXiv:1604.06647v3 [hep-th]

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In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor, calculate the one-loop effective potential of the (pseudo)tensor field, and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking.We also argue that, contrarily to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined potential and thus do not allow for the dynamical Lorentz symmetry breaking.