Comments on Foliated Gauge Theories and Dualities in 3+1d

Abstract

We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent hybrid fracton models. These field theories describe Abelian or non-Abelian gauge theories coupled to foliated gauge fields, and they fall into two classes of models that we call the electric models and the magnetic models. We show that these two classes of foliated field theories enjoy a duality. We also construct a model (using foliated gauge fields and an exactly solvable lattice Hamiltonian model) for a subsystem-symmetry protected topological (SSPT) phase, which is analogous to a one-form symmetry protected topological phase, with the subsystem symmetry acting on codimension-two subregions. We construct the corresponding gauged SSPT phase as a foliated two-form gauge theory. Some instances of the gauged SSPT phase are a variant of the X-cube model with the same ground state degeneracy and the same fusion, but different particle statistics.

57+10 pages, 7+1 figures, 2 tables

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Cited by in corpus (26)

• The low-energy limit of some exotic lattice theories and UV/IR mixing
• Anomaly Inflow for Subsystem Symmetries
• Subsystem Non-Invertible Symmetry Operators and Defects
• Non-Abelian Hybrid Fracton Orders
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
• Foliated BF theories and Multipole symmetries
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Fractons and exotic symmetries from branes
• Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge theory and anomaly inflow for subsystem symmetry
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Foliated-Exotic Duality in Fractonic BF Theories
• Gapped Lineon and Fracton Models on Graphs
• Gauging Lie group symmetry in (2+1)d topological phases
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Fractons on Graphs and Complexity
• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions
• Fractonic self-duality and covariant magnetic fractons
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Non-invertible symmetries in finite-group gauge theory
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• Exotic theta terms in 2+1d fractonic field theory