Covariant fracton gauge theory with boundary

TL;DR

This paper explores how introducing a boundary in a 4D covariant rank-2 gauge theory leads to a 3D theory with a Maxwell-Chern-Simons-like structure, revealing new boundary symmetries and conservation laws related to fracton physics.

Contribution

It demonstrates the emergence of a Maxwell-Chern-Simons-like boundary theory from a 4D covariant fracton gauge theory and uncovers associated boundary symmetries and algebraic structures.

Findings

Boundary induces a Maxwell-Chern-Simons-like 3D theory.

Boundary exhibits a generalized U(1) Kaf-Moody algebra.

Boundary theory conserves the dipole moment.

Abstract

In this paper we study the consequences of the introduction of a flat boundary on a 4D covariant rank-2 gauge theory described by a linear combination of linearized gravity and covariant fracton theory. We show that this theory gives rise to a Maxwell-Chern-Simons-like theory of two rank-2 traceless symmetric tensor fields. This induced 3D theory can be physically traced back to the traceless scalar charge theory of fractons, where the Chern-Simons-like term plays the role of a matter contribution. By further imposing time reversal invariance on the boundary, the Chern-Simons-like term disappears. Importantly, on the boundary of our 4D gauge theory we find a generalized U(1) Ka\c{c}-Moody algebra and the induced 3D theory is characterized by the conservation of the dipole moment.