6d $ \mathcal{N}=\left(1,\;0\right) $ theories on S1/T2 and class S theories: part II

Ohmori, Kantaro; Shimizu, Hiroyuki; Tachikawa, Yuji; Yonekura, Kazuya

doi:10.1007/JHEP12(2015)131

Title: 6d $$ \mathcal{N}=\left(1,\;0\right) $$ theories on S¹/T² and class S theories: part II

Abstract

Here, we study the T² compactification of a class of 6d $$ \mathcal{N}=\left(1,\;0\right) $$ theories that is Higgsable to $$ \mathcal{N}=\left(2,\;0\right) $$ theories. We show that the resulting 4d 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 SL(2,Z) 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.

Authors:

Ohmori, Kantaro ^[1]; Shimizu, Hiroyuki ^[1]; Tachikawa, Yuji ^[2]; Yonekura, Kazuya ^[3]

Univ. of Tokyo, Tokyo (Japan)
Univ. of Tokyo, Tokyo (Japan); Univ. of Tokyo, Chiba (Japan)
Univ. of Tokyo, Chiba (Japan); Institute for Advanced Study, Princeton, NJ (United States)

Publication Date:: Mon Dec 21 00:00:00 EST 2015

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1435147

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: 12; 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 S1/T2 and class S theories: part II.  United States: N. p., 2015. 
Web.  doi:10.1007/JHEP12(2015)131.

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                    Ohmori, Kantaro, Shimizu, Hiroyuki, Tachikawa, Yuji, & Yonekura, Kazuya. 6d $ \mathcal{N}=\left(1,\;0\right) $ theories on S1/T2 and class S theories: part II.  United States.  https://doi.org/10.1007/JHEP12(2015)131

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                    Ohmori, Kantaro, Shimizu, Hiroyuki, Tachikawa, Yuji, and Yonekura, Kazuya. Mon .  
"6d $ \mathcal{N}=\left(1,\;0\right) $ theories on S1/T2 and class S theories: part II".  United States.  https://doi.org/10.1007/JHEP12(2015)131.  https://www.osti.gov/servlets/purl/1435147.

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@article{osti_1435147,

  title        = {6d $ \mathcal{N}=\left(1,\;0\right) $ theories on S1/T2 and class S theories: part II},

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

  abstractNote = {Here, we study the T2 compactification of a class of 6d $ \mathcal{N}=\left(1,\;0\right) $ theories that is Higgsable to $ \mathcal{N}=\left(2,\;0\right) $ theories. We show that the resulting 4d 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 SL(2,Z) 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.},

  doi          = {10.1007/JHEP12(2015)131},

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

  number       = 12,

  volume       = 2015,

  place        = {United States},

  year         = {Mon Dec 21 00:00:00 EST 2015},

  month        = {Mon Dec 21 00:00:00 EST 2015}

}

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Works referencing / citing this record:

S 1 /T 2 compactifications of 6d N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ theories and brane webs
journal, March 2016

Ohmori, Kantaro; Shimizu, Hiroyuki
Journal of High Energy Physics, Vol. 2016, Issue 3
DOI: 10.1007/jhep03(2016)024

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Title: 6d $$ \mathcal{N}=\left(1,\;0\right) $$ theories on S1/T2 and class S theories: part II

Abstract

Citation Formats

N = 2 dualities journal, August 2012

Geometric engineering, mirror symmetry and 6 d 1 0 → 4 d N = 2 $$ 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} $$ journal, November 2015

Classification of 6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ gauge theories journal, November 2015

Topological strings and 5d T N partition functions journal, June 2014

Branes, superpotentials and superconformal fixed points journal, October 1997

Mass-deformed T N as a linear quiver journal, February 2015

Exact partition functions of Higgsed 5d T N theories journal, January 2015

6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ theories on T2 and class S theories. Part I journal, July 2015

OnS-duality in Abelian gauge theory journal, September 1995

On the 6d origin of discrete additional data of 4d gauge theories journal, May 2014

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD journal, December 1994

Topological vertex for Higgsed 5d T N theories journal, September 2015

M5-Branes, D4-Branes and quantum 5D super-Yang-Mills journal, January 2011

The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD journal, July 1996

Webs of ( p , q ) 5-branes, five dimensional field theories and grid diagrams journal, January 1998

Tinkertoys for the E 6 theory journal, September 2015

6d Conformal matter journal, February 2015

Generalized Green-Schwarz mechanism in F theory journal, November 1996

Central charges of 𝒩 = 2 superconformal field theories in four dimensions journal, September 2008

Holography for (1,0) theories in six dimensions journal, December 2014

Lifting 4d dualities to 5d journal, April 2015

Tinkertoys for Gaiotto duality journal, November 2010

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories journal, July 2015

Webs of five-branes and 𝒩 = 2 superconformal field theories journal, September 2009

The gravity duals of $ \mathcal{N}=2 $ superconformal field theories journal, October 2012

On the classification of 6D SCFTs and generalized ADE orbifolds journal, May 2014

NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES journal, February 2013

Tinkertoys for the D N series journal, February 2013

Five-branes, seven-branes and five-dimensional E n field theories journal, March 1999

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory journal, September 1994

Atomic classification of 6D SCFTs: Atomic classification of 6D SCFTs journal, June 2015

S-duality in N = 2 supersymmetric gauge theories journal, December 2007

Lagrangians of N = 2 supergravity-matter systems journal, January 1985

6D SCFTs and gravity journal, June 2015

6d, N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ Coulomb branch anomaly matching journal, October 2014

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Title: 6d $$ \mathcal{N}=\left(1,\;0\right) $$ theories on S¹/T² and class S theories: part II

N = 2 dualities
journal, August 2012

Geometric engineering, mirror symmetry and 6 d 1 0 → 4 d N = 2 $$ 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} $$
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Classification of 6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ gauge theories
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Topological strings and 5d T N partition functions
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Branes, superpotentials and superconformal fixed points
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Mass-deformed T N as a linear quiver
journal, February 2015

Exact partition functions of Higgsed 5d T N theories
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6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ theories on T2 and class S theories. Part I
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OnS-duality in Abelian gauge theory
journal, September 1995

On the 6d origin of discrete additional data of 4d gauge theories
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Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
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Topological vertex for Higgsed 5d T N theories
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The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD
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Tinkertoys for the E 6 theory
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Central charges of 𝒩 = 2 superconformal field theories in four dimensions
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journal, December 2014

Lifting 4d dualities to 5d
journal, April 2015

Tinkertoys for Gaiotto duality
journal, November 2010

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories
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Webs of five-branes and 𝒩 = 2 superconformal field theories
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The gravity duals of $ \mathcal{N}=2 $ superconformal field theories
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On the classification of 6D SCFTs and generalized ADE orbifolds
journal, May 2014

NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES
journal, February 2013

Tinkertoys for the D N series
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Five-branes, seven-branes and five-dimensional E _n field theories
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