# Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

### Submission summary

 As Contributors: Clay Cordova · Po-Shen Hsin · Nathan Seiberg Arxiv Link: https://arxiv.org/abs/1711.10008v2 (pdf) Date accepted: 2018-04-05 Date submitted: 2018-02-15 01:00 Submitted by: Cordova, Clay Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approach: Theoretical

### Abstract

We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete $\theta$-parameters, which control the weights in the sum over topologically distinct gauge bundles. We derive level-rank duality for these topological field theories. Our results may also be viewed as level-rank duality for $SO(N)_{K}$ Chern-Simons theory in the presence of background fields for discrete global symmetries. In particular, we include the required counterterms and analysis of the anomalies. We couple our theories to charged matter and determine how these counterterms are shifted by integrating out massive fermions. By gauging discrete global symmetries we derive new boson-fermion dualities for vector matter, and present the phase diagram of theories with two-index tensor fermions, thus extending previous results for $SO(N)$ to other global forms of the gauge group.

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 4, 021 (2018)

### Submission & Refereeing History

Submission 1711.10008v2 on 15 February 2018

## Reports on this Submission

### Anonymous Report 1 on 2018-2-21 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1711.10008v2, delivered 2018-02-21, doi: 10.21468/SciPost.Report.355

### Strengths

1-The paper speaks to a very topical set of questions: dualities in 2+1 dimensional topological and conformal field theories based on Chern-Simons gauge theories.

2-The paper concerns itself exclusively with subtleties regarding discrete global 0-form and 1-form theories in gauge theories based on various groups based on SO(N) Lie algebras. These questions require considerable care and the paper does an amazing job in carefully covering all possible angles on the problem and is extremely well written. This will be a very helpful reference work for anyone who ever wants to know anything about these issues.

### Weaknesses

1 - The paper concerns itself exclusively with subtleties regarding discrete global 0-form and 1-form theories based on various groups based on SO(N) Lie algebras.

### Report

This is a rather technical paper, but it is does a very careful job at exhaustively covering the field and should be published.

### Requested changes

1- no specific change.

• validity: top
• significance: good
• originality: high
• clarity: top
• formatting: excellent
• grammar: perfect