SU(N) - symmetric dynamic aether: General formalism and a hypothesis on spontaneous color polarization

TL;DR

This paper develops a comprehensive SU(N)-symmetric dynamic aether model incorporating Yang-Mills fields and explores a hypothesis that spontaneous color polarization leads to anisotropic color space through a phase transition.

Contribution

It formulates a new SU(N)-symmetric aether model with constitutive tensors and derives the full set of master equations, introducing a hypothesis on spontaneous color polarization.

Findings

Reconstructed the constitutive tensors for the SU(N) aether model.

Derived the self-consistent system of master equations for gauge, vector, and gravitational fields.

Proposed a hypothesis that spontaneous color polarization causes anisotropic color space.

Abstract

The SU(N)-symmetric generalization of the model of the electromagnetically active dynamic aether is formulated. This generalization is based on the introduction of a Yang-Mills gauge field instead of the Maxwell field, and of a SU(N)-multiplet of vector fields instead of the standard single vector field. In the framework of the second order version of the effective field theory this generalization includes three constitutive tensors, which are the SU(N) extensions of the tensors appeared in the Einstein-Maxwell-aether theory; we reconstructed the full-format set of these constitutive tensors. The total self-consistent system of master equations for the gauge, vector and gravitational fields is obtained by the variation procedure. The general model of the SU(N)-symmetric dynamic aether is reduced to the extended Einstein-Yang-Mills-aether model by the ansatz about spontaneous color polarization of the vector fields. In fact, this ansatz requires the vector fields, which form the SU(N) multiplet, to become parallel in the group (color) space due to a phase transition, and a new selected direction in the group space to appear, thus converting it into the anisotropic color space.