# 6d $$ \mathcal{N}=\left(1,0\right) $$ theories on T ^{2} and class S theories. Part I

## Abstract

We show that the N=(1,0) superconformal theory on a single M _{5} brane on the ALE space of type G = A _{n}, D _{n}, E _{n}, when compactified on T ^{2}, becomes a class S theory of type G on a sphere with two full punctures and a simple puncture. We study this relation from various viewpoints. Along the way, we develop a new method to study the 4d SCFT arising from the T ^{2} compactification of a class of 6d N=(1,0) theories we call very Higgsable.

- Authors:

- University of Tokyo, Bunkyo-ku (Japan). Department of Physics, Faculty of Science
- University of Tokyo, Bunkyo-ku (Japan). Department of Physics, Faculty of Science; University of Tokyo, Kashiwa (Japan). Institute for the Physics and Mathematics of the Universe
- Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

- Publication Date:

- Research Org.:
- Inst. for Advanced Study, Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1454726

- Grant/Contract Number:
- SC0009988

- Resource Type:
- Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 7; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Duality in Gauge Field Theories; Field Theories in Higher Dimensions

### Citation Formats

```
Ohmori, Kantaro, Shimizu, Hiroyuki, Tachikawa, Yuji, and Yonekura, Kazuya. 6d $ \mathcal{N}=\left(1,0\right) $ theories on T2 and class S theories. Part I. United States: N. p., 2015.
Web. doi:10.1007/JHEP07(2015)014.
```

```
Ohmori, Kantaro, Shimizu, Hiroyuki, Tachikawa, Yuji, & Yonekura, Kazuya. 6d $ \mathcal{N}=\left(1,0\right) $ theories on T2 and class S theories. Part I. United States. doi:10.1007/JHEP07(2015)014.
```

```
Ohmori, Kantaro, Shimizu, Hiroyuki, Tachikawa, Yuji, and Yonekura, Kazuya. Mon .
"6d $ \mathcal{N}=\left(1,0\right) $ theories on T2 and class S theories. Part I". United States. doi:10.1007/JHEP07(2015)014. https://www.osti.gov/servlets/purl/1454726.
```

```
@article{osti_1454726,
```

title = {6d $ \mathcal{N}=\left(1,0\right) $ theories on T2 and class S theories. Part I},

author = {Ohmori, Kantaro and Shimizu, Hiroyuki and Tachikawa, Yuji and Yonekura, Kazuya},

abstractNote = {We show that the N=(1,0) superconformal theory on a single M5 brane on the ALE space of type G = A n, D n, E n, when compactified on T2, becomes a class S theory of type G on a sphere with two full punctures and a simple puncture. We study this relation from various viewpoints. Along the way, we develop a new method to study the 4d SCFT arising from the T2 compactification of a class of 6d N=(1,0) theories we call very Higgsable.},

doi = {10.1007/JHEP07(2015)014},

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

number = 7,

volume = 2015,

place = {United States},

year = {2015},

month = {7}

}

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