Field Theories With a Vector Global Symmetry

TL;DR

This paper investigates nonrelativistic field theories with vector global symmetries, exploring their properties, examples, and couplings to gauge fields, motivated by fracton physics and extending known symmetry concepts.

Contribution

It introduces and analyzes nonrelativistic field theories with vector global symmetries, including their current equations, examples, and gauge couplings, expanding the understanding of such symmetries.

Findings

Different types of vector global symmetries are presented.

Examples include relativistic one-form symmetries and their nonrelativistic counterparts.

Couplings to gauge fields are discussed and related to known models.

Abstract

Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They differ by the equations their Noether currents satisfy. Simple cases, other than the translation symmetry, are an ordinary (relativistic) one-form global symmetry and its nonrelativistic generalization. In the latter case the conserved charge is associated with a codimension-one spatial manifold, but it is not topological. More general examples involve charges that are integrated over the entire space. We also discuss the coupling of these systems to gauge fields for these symmetries. We relate our examples to known continuum and lattice constructions.