Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is hybrid between symmetric higher-rank theory (i.e., higher-spin theory) and anti-symmetric topological theory. Our describes mixed unitary phase interplaying gapless gapped order phases (which can live with or without Euclidean, Poincar\'e anisotropic symmetry, at least ultraviolet high intermediate energy theory, but not yet to lattice cutoff scale). The "gauge structure" be compact, continuous, abelian non-abelian. sits outside the paradigm Maxwell electromagnetic 1865 Yang-Mills isospin/color 1954. discuss its local transformation terms ungauged vector-like tensor-like higher-moment global symmetry. non-abelian structure caused by gauging non-commutative symmetries: symmetry charge conjugation (particle-hole) Vector symmetries along time direction may exhibit crystals. explore relation these long-range entangled matters generalization Fracton condensed matter, formulation foliation, spacetime embedding Embeddon we newly introduce, possible fundamental physics applications dark matter energy.