Anomaly Inflow for Subsystem Symmetries

Abstract

We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for ordinary global symmetries, anomalies for subsystem symmetries can be canceled by anomaly inflow from a bulk theory in one higher dimension; the corresponding bulk is therefore a non-trivial subsystem symmetry protected topological (SSPT) phase. We demonstrate these phenomena in several examples with continuous and discrete subsystem global symmetries, as well as time-reversal symmetry. For each example we describe the boundary anomaly, and present classical continuum actions for the corresponding bulk SSPT phases, which describe the response of background gauge fields associated with the subsystem symmetries. Interestingly, we show that the anomaly does not uniquely specify the bulk SSPT phase. In general, the latter may also depend on how the symmetry and the associated foliation structure on the boundary are extended into the bulk.

41 pages, 2 figures; the authors were ordered alphabetically

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Cited by in corpus (43)

• Generalized Symmetries in Condensed Matter
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Subsystem Non-Invertible Symmetry Operators and Defects
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
• Foliated BF theories and Multipole symmetries
• Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge theory and anomaly inflow for subsystem symmetry
• Boson-fermion duality with subsystem symmetry
• Boundary theory of the X-cube model in the continuum
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• A Chern-Simons theory for dipole symmetry
• Foliated-Exotic Duality in Fractonic BF Theories
• Covariant fracton gauge theory with boundary
• Gapped Lineon and Fracton Models on Graphs
• Multipole and fracton topological order via gauging foliated SPT phases
• Gapped boundaries of (3+1)d topological orders
• Fractons on Graphs and Complexity
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions
• Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Anomalies in Covariant Fracton Theories
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• A Multicritical Point with Infinite Fractal Symmetries
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Fractonic superfluids. III. Hybridizing higher moments
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Topological Dipole Insulator
• Covariant Fractons and Weitzenböck Torsion
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Exotic theta terms in 2+1d fractonic field theory
• Matrix product state classification of 1D multipole symmetry protected topological phases
• Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass