Exotic $\mathbb{Z}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory

Abstract: Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the low-energy physics of the X-cube model. A key aspect of our constructions is the use of discontinuous fields in the continuum field theory. Spacetime is continuous, but the fields are not.