Dynamical Lorentz symmetry breaking from a(3+1)-dimensional axion-Wess-Zumino model

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Abstract
We study renormalizable Abelian vector-field models in the presence of the Wess-Zumino interaction with pseudoscalar matter. Renormalizability is achieved by supplementing the standard kinetic term of vector fields with higher derivatives. The appearance of a fourth power of momentum in the vector-field propagator leads to the superrenormalizable theory in which the β function, the vector-field renormalization constant, and the anomalous mass dimension are calculated exactly. It is shown that this model has the infrared stable fixed point and its low-energy limit is nontrivial. The modified effective potential for the pseudoscalar matter leads to the possible occurrence of dynamical breaking of Lorentz symmetry. This phenomenon is related to the modification of electrodynamics by means of the Chern-Simons (CS) interaction polarized along a constant CS vector. Its presence makes the vacuum that has been recently estimated from astrophysical data optically active. We examine two possibilities for the CS vector to be timelike or spacelike, under the assumption that it originates from VEV of some pseudoscalar matter and show that only the latter one naturally arises in the framework of the present model.
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