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The SU(N)-symmetric generalization of the model of the electromagneticallyactive dynamic aether is formulated. This generalization is based on theintroduction of a Yang-Mills gauge field instead of the Maxwell field, and of aSU(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 thisgeneralization includes three constitutive tensors, which are the SU(N)extensions of the tensors appeared in the Einstein-Maxwell-aether theory; wereconstructed the full-format set of these constitutive tensors. The totalself-consistent system of master equations for the gauge, vector andgravitational fields is obtained by the variation procedure. The general modelof the SU(N)-symmetric dynamic aether is reduced to the extendedEinstein-Yang-Mills-aether model by the ansatz about spontaneous colorpolarization of the vector fields. In fact, this ansatz requires the vectorfields, 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 groupspace to appear, thus converting it into the anisotropic color space.

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