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Field Theories With a Vector Global Symmetry

by Nathan Seiberg

Submission summary

As Contributors: Nathan Seiberg
Arxiv Link: https://arxiv.org/abs/1909.10544v1
Date submitted: 2020-01-06
Submitted by: Seiberg, Nathan
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Quantum Physics
Approach: Theoretical

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.

Current status:
Editor-in-charge assigned


Submission & Refereeing History

Submission 1909.10544v1 on 6 January 2020

Reports on this Submission

Anonymous Report 1 on 2020-2-11 Invited Report

Strengths

1 - Provides a more general perspective on field theories with conserved vector charges than is present in the fracton literature.
2 - Unites fracton theories with other more familiar types of field theories, such as higher form gauge theories.
3 - Provides an interesting complementary perspective to other recent treatments on getting fracton theories from vector gauge theories.

Weaknesses

No particular weaknesses.

Report

In this interesting paper, the author explores the properties of a new class of field theories with conserved vector charges. Several examples of these theories had been studied previously in the context of fractons, but this paper approaches these theories from a more general perspective and constructs several new examples. This paper will not only be of interest to the fracton community, but should be of general interest to the broader field theory community. I find this work to be a notable addition to the literature, and I recommend it for publication without any revisions.

Requested changes

No changes necessary.

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: perfect
  • grammar: perfect

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