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

Journal Article · Fri Jan 15 04:00:00 EST 2021 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2020.168370· OSTI ID:23183262

Wang, Juven ^[1]; Xu, Kai ^[2]

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1. Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138 (United States)
2. Department of Mathematics, Harvard University, Cambridge, MA 02138 (United States)

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, Poincaré, 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.

• OSTI ID: 23183262
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 424; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANISOTROPY
CRYSTALS
EUCLIDEAN SPACE
GAUGE INVARIANCE
ISOSPIN
NONLUMINOUS MATTER
QUANTUM ENTANGLEMENT
QUANTUM FIELD THEORY
SPACE-TIME
SPIN
SYMMETRY
TENSOR FIELDS
TOPOLOGY
ULTRAVIOLET RADIATION
VECTORS