Anomaly inflow for dipole symmetry and higher form foliated field theories

TL;DR

This paper explores novel topological phases with multipole symmetries, introducing higher-dimensional BF theories that reveal unique braiding statistics, ground state degeneracies, and anomaly inflow mechanisms in fracton-like systems.

Contribution

It introduces a new class of $(d+1)$-dimensional BF theories with $p$-form gauge fields that model dipole and multipole symmetries, revealing their physical properties and anomalies.

Findings

Gauge invariant loops have position-dependent braiding statistics.

Ground state degeneracy depends on system size in a novel way.

Theories exhibit a mixed 't Hooft anomaly canceled by an inflow mechanism.

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.