Emergent fracton strings from covariant bi-form gauge field theory

TL;DR

This paper develops a covariant tensor gauge field theory that naturally produces fracton-like string excitations, revealing deep connections between fractonic matter, higher-rank gauge fields, and gravity.

Contribution

It introduces a covariant framework for rank-4 tensor gauge fields that generates fractonic strings and links to linearised area-metric gravity, unifying fracton and gravitational theories.

Findings

Derives Maxwell-like equations for fractonic strings from symmetry principles.

Identifies a new generalized dipole conservation law restricting string mobility.

Connects fractonic string excitations to linearised area-metric gravity.

Abstract

We present a covariant field-theoretical framework for a rank-4 tensor gauge field theory describing fractonic string-like objects. We show that the most general quadratic, parity-preserving action naturally leads to a Maxwell-like sector, with tensorial analogues of electric and magnetic fields, Maxwell-like equations, a conserved energy-momentum tensor, and a Lorentz-like force. Remarkably, the theory gives rise to fracton-like string excitations purely from symmetry principles: constraints on the motion of these extended objects appear as Gauss-like laws, without being imposed by hand. One of these laws is new and corresponds to a generalised dipole conservation for closed strings, restricting their mobility and defining a novel class of fractonic string-like excitations. Finally, we uncover a connection to linearised area-metric gravity: in a suitable limit, the theory reduces to known covariant fracton models with rank-2 gauge fields, highlighting a deep link between fractonic matter and gravity-like structures. This provides a unified perspective on higher-rank gauge fields, extended excitations, and emergent gravitational features.