Anomaly inflow for dipole symmetry and higher form foliated field theories

Abstract

In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied -- multipole symmetry, associated with conservation of multipoles. Based on algebraic relation between dipole and global charges, we introduce a series of $(d+1)$-dimensional BF theories with $p$-form gauge fields, which admit dipole of spatially extended excitations, and study their physical properties. We elucidate that gauge invariant loops have unusual form, containing linear function of the spatial coordinate, which leads to the position dependent braiding statistics and unusual ground state degeneracy dependence on the system size. We also show that the theories exhibit a mixed 't Hooft anomaly between $p$-form and $(d-p)$-form dipole symmetries, which is canceled by an invertible theory defined in one dimensional higher via anomaly inflow mechanism.

29 pages, 3figures

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Cited by in corpus (8)

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Noninvertible operators in one, two, and three dimensions via gauging spatially modulated symmetry
• Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• ${\mathbb{Z}}_N$ generalizations of three-dimensional stabilizer codes
• Emergent fracton strings from covariant bi-form gauge field theory
• Matrix product state classification of 1D multipole symmetry protected topological phases
• Non-invertible translation from Lieb-Schultz-Mattis anomaly