# 4d $$ \mathcal{N} $$=2 theories with disconnected gauge groups

## Abstract

In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1 $$ \mathcal{N} $$ = 2 SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 $$ \mathcal{N} $$ = 2 SCFTs. The global symmetries that can be gauged involve a non-trivial combination of discrete subgroups of the U(1) _{R}, low-energy EM duality group SL(2,Z), and the outer automorphism group of the flavor symmetry algebra, Out(F ). The theories that we construct are remarkable in many ways: (i) two of them have exceptional F _{4} and G _{2} flavor groups; (ii) they substantially complete the picture of the landscape of rank-1 $$ \mathcal{N} $$ = 2 SCFTs as they realize all but one of the remaining consistent rank-1 Seiberg-Witten geometries that we previously constructed but were not associated to known SCFTs; and (iii) some of them have enlarged $$ \mathcal{N} $$ = 3 SUSY, and have not been previously constructed. They are also examples of SCFTs which violate the ShapereTachikawa relation between the conformal central charges and the scaling dimension of the Coulomb branch vev. Here, we propose a modification of the formulas computing these central charges from the topologically twisted Coulomb branch partition function which correctly compute them for discretely gauged theories.

- Authors:

- Univ. of Cincinnati, Cincinnati, OH (United States)

- Publication Date:

- Research Org.:
- Univ. of Cincinnati, Cincinnati, OH (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1361193

- Grant/Contract Number:
- SC0011784

- 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: 3; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal field theory; discrete symmetries; extended supersymmetry; supersymmetry and duality

### Citation Formats

```
Argyres, Philip C., and Martone, Mario.
```*4d $ \mathcal{N} $=2 theories with disconnected gauge groups*. United States: N. p., 2017.
Web. doi:10.1007/JHEP03(2017)145.

```
Argyres, Philip C., & Martone, Mario.
```*4d $ \mathcal{N} $=2 theories with disconnected gauge groups*. United States. doi:10.1007/JHEP03(2017)145.

```
Argyres, Philip C., and Martone, Mario. Tue .
"4d $ \mathcal{N} $=2 theories with disconnected gauge groups". United States.
doi:10.1007/JHEP03(2017)145. https://www.osti.gov/servlets/purl/1361193.
```

```
@article{osti_1361193,
```

title = {4d $ \mathcal{N} $=2 theories with disconnected gauge groups},

author = {Argyres, Philip C. and Martone, Mario},

abstractNote = {In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1 $ \mathcal{N} $ = 2 SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 $ \mathcal{N} $ = 2 SCFTs. The global symmetries that can be gauged involve a non-trivial combination of discrete subgroups of the U(1)R, low-energy EM duality group SL(2,Z), and the outer automorphism group of the flavor symmetry algebra, Out(F ). The theories that we construct are remarkable in many ways: (i) two of them have exceptional F4 and G2 flavor groups; (ii) they substantially complete the picture of the landscape of rank-1 $ \mathcal{N} $ = 2 SCFTs as they realize all but one of the remaining consistent rank-1 Seiberg-Witten geometries that we previously constructed but were not associated to known SCFTs; and (iii) some of them have enlarged $ \mathcal{N} $ = 3 SUSY, and have not been previously constructed. They are also examples of SCFTs which violate the ShapereTachikawa relation between the conformal central charges and the scaling dimension of the Coulomb branch vev. Here, we propose a modification of the formulas computing these central charges from the topologically twisted Coulomb branch partition function which correctly compute them for discretely gauged theories.},

doi = {10.1007/JHEP03(2017)145},

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

number = 3,

volume = 2017,

place = {United States},

year = {Tue Mar 28 00:00:00 EDT 2017},

month = {Tue Mar 28 00:00:00 EDT 2017}

}

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