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

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, 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.

40 pages, 8 figures, 4 tables. v3: Refinement, Refs added, and minor corrections. See also arXiv:1911.01804. Our new theory is dedicated to 90 years of Gauge Principle since Hermann Weyl and 65 years of Yang-Mills theory

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• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Twisted Gauge Theory Model of Topological Phases in Three Dimensions
• Quantum Statistics and Spacetime Topology: Quantum Surgery Formulas

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• Boson-fermion duality with subsystem symmetry
• A symmetry principle for gauge theories with fractons
• Fracton Self-Statistics
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Asymptotic symmetries and soft charges of fractons
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Non-Abelian fracton order from gauging a mixture of subsystem and global symmetries
• Shift symmetries and duality web in gauge theories