SciPost logo

SciPost Submission Page

Field Theories With a Vector Global Symmetry

by Nathan Seiberg

This Submission thread is now published as SciPost Phys. 8, 050 (2020)

Submission summary

As Contributors: Nathan Seiberg
Arxiv Link: (pdf)
Date accepted: 2020-03-12
Date submitted: 2020-01-06 01:00
Submitted by: Seiberg, Nathan
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

Ontology / Topics

See full Ontology or Topics database.

Global symmetries

Published as SciPost Phys. 8, 050 (2020)

Submission & Refereeing History

Published as SciPost Phys. 8, 050 (2020)

Reports on this Submission

Anonymous Report 2 on 2020-2-24 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1909.10544v1, delivered 2020-02-24, doi: 10.21468/SciPost.Report.1542


The author considers non-relativistic field theories with global symmetries giving rise to vector conserved charges, motivated by the discussions of fractons. It is not very common in the high energy field theory community to look at non-relativistics systems, and it is also not so common in the condensed matter community to adhere to the field theory language based on model independent symmetry principles that the author so clearly and helpfully follows. Therefore this work will be valuable for both communities, and I recommend its publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2020-2-11 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1909.10544v1, delivered 2020-02-11, doi: 10.21468/SciPost.Report.1490


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.


No particular weaknesses.


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

Login to report or comment