Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory

TL;DR

The paper develops a 3+1D continuum framework for exotic $U(1)$ symmetries and fracton-like behavior by analyzing four interrelated theories: the $\phi$-theory, its dual $\hat{\phi}$, and two tensor gauge theories $A$ and $\hat{A}$. It reveals rich spectra of momentum and winding states, along with corresponding tensorial and dipole global symmetries, and demonstrates nontrivial dualities that exchange momentum and winding modes and electric/magnetic sectors between dual pairs. The work also connects lattice XY-plaquette constructions to their continuum descriptions, shows how defects realize fracton-like mobility constraints, and establishes robustness/universality of the low-energy features under higher-derivative deformations. These results lay groundwork for a continuum understanding of fracton physics in 3+1D and set the stage for later $\mathbb{Z}_N$ generalizations and connections to models like the X-cube in subsequent work.

Abstract

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 $\mathbb{Z}_N$ symmetry.