Higher-spin Witten effect and two-dimensional fracton phases

In addition to the familiar Maxwell terms, the Lagrangian for a three-dimensional U(1) gauge theory can have an extra ``theta'' term which has two effects: attaching electric charge to magnetic monopoles in the bulk, and generating a Chern-Simons term on the boundary. This work studies theta terms in the context of higher rank tensor U(1) gauge theories, which host gapless higher-spin gauge modes and subdimensional charge excitations. There are multiple different varieties of theta terms, enforcing different types of charge attachment in the bulk. These terms also lead to generalized tensor Chern-Simons theories on the boundary, bringing about the existence of two-dimensional fracton phases.