Abstract
We consider the axion field and electromagnetic waves with rapid time dependence, coupled to a strong time independent, asymptotically approaching a constant at infinity “mean” magnetic field, which takes into account the back reaction from the axion field and electromagnetic waves with rapid time dependence in a time averaged way. The direction of the self consistent mean field is orthogonal to the common direction of propagation of the axion and electromagnetic waves with rapid time dependence and parallel to the polarization of these electromagnetic waves. Then, there is an effective U(1) symmetry mixing axions and photons. Using the natural complex variables that this U(1) symmetry suggests we find localized planar soliton solutions. These solutions appear to be stable since they produce a different magnetic flux than the state with only a constant magnetic field, which we take as our “ground state”. The solitons also have non-trivial U(1) charge defined before, different from the uncharged vacuum. These solitons represent a new, non-gravitational mechanism, of trapping light. They could also affect the vacuum structure in models of the QCD vacuum that incorporate a magnetic condensate, introducing may be gluon axion solitons.
Highlights
One of the most interesting ideas for going beyond the standard model has been the introduction of the axion [1], which provided a way to solve the strong CP problem
It will be shown that when considering the axion photon system in an self consistent, time independent magnetic field, that is one that takes into account the back reaction of the axion photon system on the magnetic field in an averaged mean field approach, we find that there are localized soliton like solutions
Since magnetic flux is conserved, we take this as an indication of the stability of this solution towards decaying into the Bx = B0 stable ”ground state”
Summary
One of the most interesting ideas for going beyond the standard model has been the introduction of the axion [1], which provided a way to solve the strong CP problem. A way to explore for observable consequences of the coupling of a light scalar to the photon in this way is to subject a beam of photons to a very strong magnetic field. This affects the optical properties of light which could lead to testable consequences[3]. In particular the results of [5] imply that an external constant magnetic field in the axion photon system is a stable vacuum under small perturbations. This is in contrast to an external electric field, which exhibits tachyonic instabilities [5]. The resulting planar soliton solutions that are obtained appear to be stable since they produce a different magnetic flux than configuration where the localized axion photon configuration is absent, that is, when we have just the a constant magnetic field all over space (our choice of stable vacuum)
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