# Chern-Simons-matter dualities with SO and USp gauge groups

## Abstract

In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between SO(N) _{k} Chern-Simons theories coupled to N _{f} real scalars in the fundamental representation, and SO(k)- _{N+N} _{f} _{/2} coupled to N _{f} real (Majorana) fermions in the fundamental. For N _{f} = 0 these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. As a result, for *k* = 1 we get an interesting low-energy duality between N _{f} free Majorana fermions and an SO( *N*) _{1} Chern-Simons theory coupled to N _{f} scalar fields (with N _{f} ≤ *N*-2).

- Authors:

- Weizmann Institute of Science, Rehovot (Israel)
- Institute for Advanced Study, Princeton, NJ (United States); Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste (Italy)
- Princeton Univ., Princeton, NJ (United States)
- Institute for Advanced Study, Princeton, NJ (United States)

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States); Weizmann Inst. of Science, Rehovot (Israel)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1356080

- Alternate Identifier(s):
- OSTI ID: 1358369

- Grant/Contract Number:
- SC0009988

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; group-level duality; mirror symmetry; field-theory; dimensions; models; algebras; matter; chern-simons theories; conformal field theory; duality in gauge field theories; topological states of matter; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chern-Simons Therories

### Citation Formats

```
Aharony, Ofer, Benini, Francesco, Hsin, Po -Shen, and Seiberg, Nathan.
```*Chern-Simons-matter dualities with SO and USp gauge groups*. United States: N. p., 2017.
Web. doi:10.1007/JHEP02(2017)072.

```
Aharony, Ofer, Benini, Francesco, Hsin, Po -Shen, & Seiberg, Nathan.
```*Chern-Simons-matter dualities with SO and USp gauge groups*. United States. doi:10.1007/JHEP02(2017)072.

```
Aharony, Ofer, Benini, Francesco, Hsin, Po -Shen, and Seiberg, Nathan. Tue .
"Chern-Simons-matter dualities with SO and USp gauge groups". United States.
doi:10.1007/JHEP02(2017)072. https://www.osti.gov/servlets/purl/1356080.
```

```
@article{osti_1356080,
```

title = {Chern-Simons-matter dualities with SO and USp gauge groups},

author = {Aharony, Ofer and Benini, Francesco and Hsin, Po -Shen and Seiberg, Nathan},

abstractNote = {In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between SO(N)k Chern-Simons theories coupled to Nf real scalars in the fundamental representation, and SO(k)-N+Nf/2 coupled to Nf real (Majorana) fermions in the fundamental. For Nf = 0 these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. As a result, for k = 1 we get an interesting low-energy duality between Nf free Majorana fermions and an SO(N)1 Chern-Simons theory coupled to Nf scalar fields (with Nf ≤ N-2).},

doi = {10.1007/JHEP02(2017)072},

journal = {Journal of High Energy Physics (Online)},

number = 2,

volume = 2017,

place = {United States},

year = {Tue Feb 14 00:00:00 EST 2017},

month = {Tue Feb 14 00:00:00 EST 2017}

}

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