Symmetric Tensor Gauge Theories on Curved Spaces

Fractons and other subdimensional particles are an exotic class of emergent quasi-particle excitations with severely restricted mobility. A wide class of models featuring these quasi-particles have a natural description in the language of symmetric tensor gauge theories, which feature conservation laws restricting the motion of particles to lower-dimensional sub-spaces, such as lines or points. In this work, we investigate the fate of symmetric tensor gauge theories in the presence of spatial curvature. We find that weak curvature can induce small (exponentially suppressed) violations on the mobility restrictions of charges, leaving a sense of asymptotic fractonic/sub-dimensional behavior on generic manifolds. Nevertheless, we show that certain symmetric tensor gauge theories maintain sharp mobility restrictions and gauge invariance on certain special curved spaces, such as Einstein manifolds or spaces of constant curvature.