Exotic U(1) symmetries, duality, and fractons in 3 + 1-dimensional quantum field theory

We extend our exploration of nonstandard continuum quantum field theories in 2 + 1 dimensions to 3 + 1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global U(1) symmetry and in a followup paper we will study models with a global ZN symmetry.