Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory

TL;DR

The paper develops a continuum framework for 2+1D quantum field theories with exotic global symmetries and discontinuous fields, connecting them to fracton-like lattice models. It introduces the XY-plaquette model, derives a continuum Lagrangian with momentum and winding dipole symmetries, and analyzes momentum and winding modes, including a self-duality between φ and φ^{xy}. It then constructs a U(1) tensor gauge theory and a Z_N tensor gauge theory, detailing their fluxes, defects, and spectrum, and showing how lattice models flow to these theories while exhibiting robust or fragile emergent symmetries depending on UV realizations. The work highlights UV/IR interplay, nonlocal charged sectors, and dualities that resemble 1+1D analogs, thereby offering universal low-energy descriptions of fracton-related systems and setting the stage for 3+1D extensions in subsequent papers.

Abstract

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.