Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon

TL;DR

This paper introduces a novel tensor gauge field theory that combines features of higher-spin and topological field theories, describing complex phases with potential implications for fundamental physics and condensed matter.

Contribution

It formulates a new class of non-abelian tensor gauge theories that generalize existing models and explore their relation to fracton order and spacetime embedding.

Findings

Describes a hybrid tensor gauge theory with mixed topological and gapless phases.

Introduces the concept of Embeddon and relates it to spacetime embedding.

Suggests potential applications to dark matter and dark energy.

Abstract

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