https://doi.org/10.1140/epjc/s10052-026-15420-w
Regular Article - Theoretical Physics
Worldline formulations of covariant fracton theories
1
Dipartimento di Fisica e Astronomia “Augusto Righi”, Università di Bologna, via Irnerio 46, 40126, Bologna, Italy
2
INFN, Sezione di Bologna, Bologna, Italy
3
Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, via Marzolo 8, 35131, Padua, Italy
4
INFN, Sezione di Padova, Padua, Italy
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
23
October
2025
Accepted:
7
February
2026
Published online:
1
March
2026
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.
© The Author(s) 2026
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
