Argyres–Douglas theories, S 1 reductions, and topological symmetries

Buican, Matthew; Nishinaka, Takahiro

doi:10.1088/1751-8113/49/4/045401

Title: Argyres–Douglas theories, S ¹ reductions, and topological symmetries

Abstract

In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A(1), A(2n-3)) and(A(1), D-2n) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S-1 regime of these indices. As expected on general grounds, our study reproduces the S-3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases-with the exception of the reduction of the (A(1), D-4) SCFTcertain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as R symmetry mixing with the topological symmetries of the direct S-1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional N = 2 superconformal U(1)(R) symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the fourdimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general Nmore » = 2 SCFTs.« less

Authors:

Buican, Matthew ^[1]; Nishinaka, Takahiro ^[1]

Rutgers Univ., Piscataway, NJ (United States)

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

Research Org.:: Rutgers Univ., Piscataway, NJ (United States)

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

OSTI Identifier:: 1437381

Grant/Contract Number:: SC0007897

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physics. A, Mathematical and Theoretical

Additional Journal Information:: Journal Volume: 49; Journal Issue: 4; Journal ID: ISSN 1751-8113

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Buican, Matthew, and Nishinaka, Takahiro. Argyres–Douglas theories, S 1 reductions, and topological symmetries.  United States: N. p., 2015. 
Web.  doi:10.1088/1751-8113/49/4/045401.

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                    Buican, Matthew, & Nishinaka, Takahiro. Argyres–Douglas theories, S 1 reductions, and topological symmetries.  United States.  https://doi.org/10.1088/1751-8113/49/4/045401

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                    Buican, Matthew, and Nishinaka, Takahiro. Mon .  
"Argyres–Douglas theories, S 1 reductions, and topological symmetries".  United States.  https://doi.org/10.1088/1751-8113/49/4/045401.  https://www.osti.gov/servlets/purl/1437381.

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@article{osti_1437381,

  title        = {Argyres–Douglas theories, S 1 reductions, and topological symmetries},

  author       = {Buican, Matthew and Nishinaka, Takahiro},

  abstractNote = {In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A(1), A(2n-3)) and(A(1), D-2n) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S-1 regime of these indices. As expected on general grounds, our study reproduces the S-3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases-with the exception of the reduction of the (A(1), D-4) SCFTcertain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as R symmetry mixing with the topological symmetries of the direct S-1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional N = 2 superconformal U(1)(R) symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the fourdimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general N = 2 SCFTs.},

  doi          = {10.1088/1751-8113/49/4/045401},

  journal      = {Journal of Physics. A, Mathematical and Theoretical},

  number       = 4,

  volume       = 49,

  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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https://doi.org/10.1088/1751-8113/49/4/045401

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Cited by: 38 works

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Figures / Tables:

Table 1: The matter fields (and charges) of the three-dimensional gauge theory that flows to the S¹ reduction of the (A₁, A_2n-3) theory.

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Works referenced in this record:

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Works referencing / citing this record:

Notes on integral identities for 3d supersymmetric dualities
journal, April 2018

Aghaei, Nezhla; Amariti, Antonio; Sekiguchi, Yuta
Journal of High Energy Physics, Vol. 2018, Issue 4
DOI: 10.1007/jhep04(2018)022

Lagrangians for generalized Argyres-Douglas theories
journal, October 2017

Benvenuti, Sergio; Giacomelli, Simone
Journal of High Energy Physics, Vol. 2017, Issue 10
DOI: 10.1007/jhep10(2017)106

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories
journal, February 2018

Buican, Matthew; Laczko, Zoltan
Physical Review Letters, Vol. 120, Issue 8
DOI: 10.1103/physrevlett.120.081601

Figures / Tables found in this record:

Table 1 (p. 13)

Table 2 (p. 18)

Table 3 (p. 18)

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Title: Argyres–Douglas theories, S 1 reductions, and topological symmetries

Abstract

Citation Formats

Figures / Tables:

New phenomena in SU(3) supersymmetric gauge theory journal, August 1995

New = 2 superconformal field theories in four dimensions journal, February 1996

Study of N = 2 superconformal field theories in 4 dimensions journal, July 1996

Comments on scaling limits of 4d $ \mathcal{N} = 2 $ theories journal, January 2011

General Argyres-Douglas theory journal, January 2013

Central charges and RG flow of strongly-coupled $ \mathcal{N}=2 $ theory journal, March 2013

Argyres-Douglas theories and S-duality journal, February 2015

Constraints on chiral operators in N = 2 $$ \mathcal{N}=2 $$ SCFTs journal, December 2014

Four Dimensional Superconformal Index from q -Deformed Two Dimensional Yang-Mills Theory journal, June 2011

Wild quiver gauge theories journal, February 2012

Quantum Higgs branches of isolated $\mathcal{N}=2$ superconformal field theories journal, October 2012

Gauge Theories and Macdonald Polynomials journal, November 2012

From 4d superconformal indices to 3d partition functions journal, October 2011

Reducing the 4d index to the S 3 partition function journal, December 2012

Relation between the 4d superconformal index and the S 3 partition function journal, September 2011

Counting chiral primaries in , superconformal field theories journal, July 2006

An Index for 4 Dimensional Super Conformal Theories journal, June 2007

Rigid supersymmetric theories in curved superspace journal, June 2011

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories journal, January 2004

The exact superconformal R-symmetry extremizes Z journal, May 2012

Notes on SUSY gauge theories on three-sphere journal, March 2011

Aspects of N = 2 supersymmetric gauge theories in three dimensions journal, August 1997

N = 2 dualities journal, August 2012

Bootstrapping the superconformal index with surface defects journal, January 2013

3d partition function as overlap of wavefunctions journal, August 2011

Mirrors of 3d Sicilian theories journal, September 2010

3D-partition functions on the sphere: exact evaluation and mirror symmetry journal, May 2012

Exact results for Wilson loops in superconformal Chern-Simons theories with matter journal, March 2010

Framed BPS states journal, January 2013

On short and semi-short representations for four-dimensional superconformal symmetry journal, September 2003

All positive energy unitary irreducible representations of extended conformal supersymmetry journal, November 1985

Counting chiral primaries in , superconformal field theories journal, July 2006

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large n Gauge Theories conference, January 2012

Rigid Supersymmetric Theories in Curved Superspace text, January 2011

3D-partition functions on the sphere: exact evaluation and mirror symmetry text, January 2011

Quantum Higgs branches of isolated N=2 superconformal field theories text, January 2012

Constraints on Chiral Operators in N=2 SCFTs text, January 2014

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Lagrangians for generalized Argyres-Douglas theories journal, October 2017

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Title: Argyres–Douglas theories, S ¹ reductions, and topological symmetries

New phenomena in SU(3) supersymmetric gauge theory
journal, August 1995

New = 2 superconformal field theories in four dimensions
journal, February 1996

Study of N = 2 superconformal field theories in 4 dimensions
journal, July 1996

Comments on scaling limits of 4d $ \mathcal{N} = 2 $ theories
journal, January 2011

General Argyres-Douglas theory
journal, January 2013

Central charges and RG flow of strongly-coupled $ \mathcal{N}=2 $ theory
journal, March 2013

Argyres-Douglas theories and S-duality
journal, February 2015

Constraints on chiral operators in N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, December 2014

Four Dimensional Superconformal Index from $q$ -Deformed Two Dimensional Yang-Mills Theory
journal, June 2011

Wild quiver gauge theories
journal, February 2012

Quantum Higgs branches of isolated $\mathcal{N}=2$ superconformal field theories
journal, October 2012

Gauge Theories and Macdonald Polynomials
journal, November 2012

From 4d superconformal indices to 3d partition functions
journal, October 2011

Reducing the 4d index to the S 3 partition function
journal, December 2012

Relation between the 4d superconformal index and the S 3 partition function
journal, September 2011

Counting chiral primaries in , superconformal field theories
journal, July 2006

An Index for 4 Dimensional Super Conformal Theories
journal, June 2007

Rigid supersymmetric theories in curved superspace
journal, June 2011

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories
journal, January 2004

The exact superconformal R-symmetry extremizes Z
journal, May 2012

Notes on SUSY gauge theories on three-sphere
journal, March 2011

Aspects of N = 2 supersymmetric gauge theories in three dimensions
journal, August 1997

N = 2 dualities
journal, August 2012

Bootstrapping the superconformal index with surface defects
journal, January 2013

3d partition function as overlap of wavefunctions
journal, August 2011

Mirrors of 3d Sicilian theories
journal, September 2010

3D-partition functions on the sphere: exact evaluation and mirror symmetry
journal, May 2012

Exact results for Wilson loops in superconformal Chern-Simons theories with matter
journal, March 2010

Framed BPS states
journal, January 2013

On short and semi-short representations for four-dimensional superconformal symmetry
journal, September 2003

All positive energy unitary irreducible representations of extended conformal supersymmetry
journal, November 1985

Counting chiral primaries in , superconformal field theories
journal, July 2006

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large n Gauge Theories
conference, January 2012

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3D-partition functions on the sphere: exact evaluation and mirror symmetry
text, January 2011

Quantum Higgs branches of isolated N=2 superconformal field theories
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Notes on integral identities for 3d supersymmetric dualities
journal, April 2018

Lagrangians for generalized Argyres-Douglas theories
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