### Abstract

Abstract: We study the T^{2} compactification of a class of 6d N=1,0$$ \mathcal{N}=\left(1,\;0\right) $$ theories that is Higgsable to N=2,0$$ \mathcal{N}=\left(2,\;0\right) $$ theories. We show that the resulting 4d N=2$$ \mathcal{N}=2 $$ theory at the origin of the Coulomb branch and the parameter space is generically given by two superconformal matter sectors coupled by an infrared-free gauge multiplet and another conformal gauge multiplet. Our analysis utilizes the 5d theories obtained by putting the same class of 6d theories on S^{1}. Our class includes, among others, the 6d theories describing multiple M5 branes on an ALE singularity, and we analyze them in detail. The resulting 4d theory has manifestly both the SL2ℤ$$ \mathrm{S}\mathrm{L}\left(2,\mathbb{Z}\right) $$ and the full flavor symmetry. We also discuss in detail the special cases of 6d theories where the infrared-free gauge multiplet is absent. In an appendix, we give a field-theoretical argument for an F-theoretic constraint that forbids a particular 6d anomaly-free matter content, as an application of our analysis.

Original language | English |
---|---|

Article number | 131 |

Pages (from-to) | 1-54 |

Number of pages | 54 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

^{1}/T

^{2}and class S theories: part II.

*Journal of High Energy Physics*,

*2015*(12), 1-54. [131]. https://doi.org/10.1007/JHEP12(2015)131

**6d N = (1,0) theories on S ^{1} /T^{2} and class S theories : part II.** / Ohmori, Kantaro; Shimizu, Hiroyuki; Tachikawa, Yuji; Yonekura, Kazuya.

Research output: Contribution to journal › Article

^{1}/T

^{2}and class S theories: part II',

*Journal of High Energy Physics*, vol. 2015, no. 12, 131, pp. 1-54. https://doi.org/10.1007/JHEP12(2015)131

^{1}/T

^{2}and class S theories: part II. Journal of High Energy Physics. 2015 Dec 1;2015(12):1-54. 131. https://doi.org/10.1007/JHEP12(2015)131

}

TY - JOUR

T1 - 6d N = (1,0) theories on S1 /T2 and class S theories

T2 - part II

AU - Ohmori, Kantaro

AU - Shimizu, Hiroyuki

AU - Tachikawa, Yuji

AU - Yonekura, Kazuya

PY - 2015/12/1

Y1 - 2015/12/1

N2 - Abstract: We study the T2 compactification of a class of 6d N=1,0$$ \mathcal{N}=\left(1,\;0\right) $$ theories that is Higgsable to N=2,0$$ \mathcal{N}=\left(2,\;0\right) $$ theories. We show that the resulting 4d N=2$$ \mathcal{N}=2 $$ theory at the origin of the Coulomb branch and the parameter space is generically given by two superconformal matter sectors coupled by an infrared-free gauge multiplet and another conformal gauge multiplet. Our analysis utilizes the 5d theories obtained by putting the same class of 6d theories on S1. Our class includes, among others, the 6d theories describing multiple M5 branes on an ALE singularity, and we analyze them in detail. The resulting 4d theory has manifestly both the SL2ℤ$$ \mathrm{S}\mathrm{L}\left(2,\mathbb{Z}\right) $$ and the full flavor symmetry. We also discuss in detail the special cases of 6d theories where the infrared-free gauge multiplet is absent. In an appendix, we give a field-theoretical argument for an F-theoretic constraint that forbids a particular 6d anomaly-free matter content, as an application of our analysis.

AB - Abstract: We study the T2 compactification of a class of 6d N=1,0$$ \mathcal{N}=\left(1,\;0\right) $$ theories that is Higgsable to N=2,0$$ \mathcal{N}=\left(2,\;0\right) $$ theories. We show that the resulting 4d N=2$$ \mathcal{N}=2 $$ theory at the origin of the Coulomb branch and the parameter space is generically given by two superconformal matter sectors coupled by an infrared-free gauge multiplet and another conformal gauge multiplet. Our analysis utilizes the 5d theories obtained by putting the same class of 6d theories on S1. Our class includes, among others, the 6d theories describing multiple M5 branes on an ALE singularity, and we analyze them in detail. The resulting 4d theory has manifestly both the SL2ℤ$$ \mathrm{S}\mathrm{L}\left(2,\mathbb{Z}\right) $$ and the full flavor symmetry. We also discuss in detail the special cases of 6d theories where the infrared-free gauge multiplet is absent. In an appendix, we give a field-theoretical argument for an F-theoretic constraint that forbids a particular 6d anomaly-free matter content, as an application of our analysis.

UR - http://www.scopus.com/inward/record.url?scp=84951794470&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951794470&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2015)131

DO - 10.1007/JHEP12(2015)131

M3 - Article

AN - SCOPUS:84951794470

VL - 2015

SP - 1

EP - 54

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 12

M1 - 131

ER -