Quasi-topological fractons: a 3D dipolar gauge theory

TL;DR

This paper introduces a 3D gauge theory with a symmetric tensor and vector field exhibiting fractonic behavior, characterized by restricted mobility of charges, despite not being fully topological.

Contribution

It develops a quasi-topological 3D gauge theory with unique gauge fixing, revealing fractonic phenomena and generalized electromagnetism with restricted charge mobility.

Findings

The theory has three degrees of freedom.

Energy-momentum tensor vanishes on-shell.

Emergence of vector charges with restricted mobility.

Abstract

We consider the theory of a generic rank-2 tensor field in three spacetime dimensions, which involves a symmetric tensor field transforming under infinitesimal diffeomorphisms, and a vector field, whose gauge transformation depends on a local vector parameter. The gauge fixing shows a non-trivial structure, and some non-intuitive possibilities are listed. Despite the fact that the theory is not topological, the energy-momentum tensor vanishes on-shell, which justifies the quasi-topological appellation we give to this theory. We show that the theory has three degrees of freedom. Moreover we find an interesting physical interpretation, which consists in a generalized planar electromagnetism and in the emergence of two vector charges with restricted mobility. These are typical fractonic behaviours which can be related to the so called traceless scalar and vector charge theories.