## SciPost Submission Page

# 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:

### Submission & Refereeing History

## 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.