Covariant field theory of 3D massive fractons

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.