New Field Theories with Foliation Structure and Subdimensional Particles from Godbillon-Vey Invariant

TL;DR

This paper introduces a new BF-like topological field theory inspired by the Godbillon-Vey invariant, modeling subdimensional particles like fractons with mobility constraints and subextensive ground state degeneracies.

Contribution

It proposes a novel foliation-based field theory with subsystem symmetries, connecting mathematical invariants to physical models of fractons and subdimensional particles.

Findings

The theory captures mobility constraints of fractons.

It explains subextensive ground state degeneracies.

Lattice models realize the low-energy behavior of the theory.

Abstract

Recently, subdimensional particles including fractons have attracted much attention from various areas. Notable features of such matter phases are mobility constraints and subextensive ground state degeneracies (GSDs). In this paper, we propose a BF-like theory motivated by the Godbillon-Vey invariant, which is a mathematical invariant of the foliated manifold. Our theory hosts subsystem higher form symmetries which manifestly ensure the mobility constraint and subextensive GSD through the spontaneous symmetry breaking. We also discuss some lattice spin models which realize the same low energy behaviours as the BF-like theory. Furthermore, we explore dynamical matter theories which are coupled to the BF-like theory.