Covariant field theory of 3D massive fractons

TL;DR

The paper addresses constructing a covariant field theory for massive fractons in 3D using a symmetric rank-2 tensor field and a CS-like term that both generates mass and acts as intrinsic fracton matter. The authors analyze propagators, DoF, and a generalized electromagnetism formulation to show two propagating modes in both massive and massless limits, with one obeying a Klein-Gordon equation, and they derive Gauss and Ampere-like laws enforcing dipole and quadrupole conservation; intrinsic fracton content is encoded in density and current sourced by the CS term, while coupling to external matter yields a second fracton sector with distinct mobility. Intrinsic fracton content is encoded in density and current sourced by the CS term, while coupling to external matter yields a second fracton sector with distinct mobility. The work provides a covariant, quasi-topological mass generation mechanism for fractons, clarifies intrinsic versus extrinsic fracton content, and lays groundwork for interactions with matter and gravity in gapped fracton phases.

Abstract

We construct a covariant and gauge-invariant theory describing massive fractons in three spacetime dimensions, based on a symmetric rank-2 tensor field. The model includes a Chern-Simons-like term that plays a dual role: it generates a topological mass for the tensor gauge field and simultaneously acts as a source of intrinsic fractonic matter. This dual mechanism is novel and leads to a propagating fractonic degree of freedom described by a massive Klein-Gordon equation. The theory propagates two degrees of freedom -- one massive, one massless -- whose number is preserved in the massless limit, in analogy with the Maxwell-Chern-Simons mechanism of Deser-Jackiw-Templeton. We analyze the resulting equations of motion and show that the intrinsic fractonic matter satisfies Gauss- and Ampère-like laws, with conserved dipole and trace of the quadrupole moment. Upon coupling to external matter, a second fractonic sector emerges, leading to a coexistence of intrinsic and extrinsic subsystems with different mobility and conservation properties. Our model provides a unified framework for describing massive fractons with internal structure, and offers a covariant setting for exploring their interactions and extensions.