Dynamical Lorentz simmetry breaking from 3+1 Axion-Wess-Zumino model

TL;DR

This paper investigates a renormalizable abelian vector-field model with Wess-Zumino interaction, revealing a non-trivial low-energy limit, dynamical Lorentz symmetry breaking, and the stability conditions of the vacuum related to Chern-Simons modifications.

Contribution

It introduces a super-renormalizable vector-field model with higher derivatives, calculates exact renormalization group functions, and explores conditions for Lorentz symmetry breaking and vacuum stability.

Findings

The model has an infrared stable fixed point.

The low-energy limit exhibits non-trivial dynamics.

Only space-like Chern-Simons vectors are consistent, avoiding vacuum instability.

Abstract

We study the renormalizable abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The renormalizability is achieved by supplementing the standard kinetic term of vector fields with higher derivatives. The appearance of fourth power of momentum in the vector-field propagator leads to the super-renormalizable theory in which the $\beta$-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 non-trivial. The modified effective potential for the pseudoscalar matter leads to the possible occurrence of dynamical breaking of the 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 optically active that has been recently estimated from astrophysical data. We examine two possibilities for the CS vector to be time-like or space-like, under the assumption that it originates from v.e.v. of some pseudoscalar matter and show that only the latter one is consistent in the framework of the AWZ model, because a time-like CS vector makes the vacuum unstable under pairs creation of tachyonic photon modes with the finite vacuum decay rate.