Worldline Formulations of Covariant Fracton Theories

TL;DR

This paper develops covariant worldline formulations for fracton gauge theories, providing a new framework to study Lorentz-breaking quasiparticles with restricted mobility through three models and their quantization.

Contribution

It introduces three worldline models for covariant fracton theories, connecting gauge structures with BRST quantization and exploring gauge-fixing methods.

Findings

Reproduces BV spectrum and BRST transformations of fracton theories

Constructs a deformation capturing nearly the entire family of covariant fracton theories

Analyzes gauge-fixing comparing BV-BRST and string field theory approaches

Abstract

We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative. These theories, which can be interpreted as linearized gravity theories invariant under longitudinal diffeomorphisms, provide a covariant framework for studying Lorentz-breaking fracton quasiparticles, which are excitations with restricted mobility due to dipole-moment conservation. We construct three worldline models. The first two are obtained by deducing their constraint structure directly from the spacetime gauge transformations. By applying BRST quantization, we show that these models reproduce the BV spectrum and the associated BRST transformations of two specific fracton theories. The third model is defined as a deformation of the second one: although free, it is analyzed by drawing inspiration from the standard treatment of interacting worldline systems, and is shown to capture almost the entire family of covariant fracton theories. Finally, we discuss the gauge-fixing, comparing the BV-BRST spacetime perspective with the worldline analogue of the ``Siegel gauge" employed in string field theory.