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Title: Argyres-Douglas theories, the Macdonald index, and an RG inequality

Abstract

Here we conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A1,A2n₋3) and (A1,D2n) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two S-dualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a non-trivial set of renormalization group flows. Moreover, we demonstrate that, for certain values of n, our conjectures imply simple operator relations involving composites built out of the SU(2)R currents and flavor symmetry moment maps, and we find a consistent picture in which these relations give rise to certain null states in the corresponding chiral algebras. In addition, we show that the Hall-Littlewood limits of our indices are equivalent to the corresponding Higgs branch Hilbert series. We explain this fact by considering the S1 reductions of our theories and showing that the equivalence follows from an inequality on monopole quantum numbers whose coefficients are fixed by data of the four-dimensional parent theories. Finally, we comment on the implications of our work for more general $N = 2$ superconformal field theories.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Rutgers Univ., Piscataway, NJ (United States). NHETC and Dept. of Physics and Astronomy; Univ. of Chicago, IL (United States). Enrico Fermi Inst.
  2. Rutgers Univ., Piscataway, NJ (United States). NHETC and Dept. of Physics and Astronomy; Kyoto Univ. (Japan). Yukawa Inst. for Theoretical Physics
Publication Date:
Research Org.:
Rutgers Univ., Piscataway, NJ (United States); Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1327220
Grant/Contract Number:  
SC0010008; SC0003883; SC0007897; SC0009924; PHY-1066293
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: 2016; Journal Issue: 2; 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; Extended Supersymmetry; Conformal and W Symmetry; Renormalization Group

Citation Formats

Buican, Matthew, and Nishinaka, Takahiro. Argyres-Douglas theories, the Macdonald index, and an RG inequality. United States: N. p., 2016. Web. doi:10.1007/JHEP02(2016)159.
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Buican, Matthew, & Nishinaka, Takahiro. Argyres-Douglas theories, the Macdonald index, and an RG inequality. United States. https://doi.org/10.1007/JHEP02(2016)159
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Buican, Matthew, and Nishinaka, Takahiro. Wed . "Argyres-Douglas theories, the Macdonald index, and an RG inequality". United States. https://doi.org/10.1007/JHEP02(2016)159. https://www.osti.gov/servlets/purl/1327220.
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@article{osti_1327220,
title = {Argyres-Douglas theories, the Macdonald index, and an RG inequality},
author = {Buican, Matthew and Nishinaka, Takahiro},
abstractNote = {Here we conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A1,A2n₋3) and (A1,D2n) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two S-dualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a non-trivial set of renormalization group flows. Moreover, we demonstrate that, for certain values of n, our conjectures imply simple operator relations involving composites built out of the SU(2)R currents and flavor symmetry moment maps, and we find a consistent picture in which these relations give rise to certain null states in the corresponding chiral algebras. In addition, we show that the Hall-Littlewood limits of our indices are equivalent to the corresponding Higgs branch Hilbert series. We explain this fact by considering the S1 reductions of our theories and showing that the equivalence follows from an inequality on monopole quantum numbers whose coefficients are fixed by data of the four-dimensional parent theories. Finally, we comment on the implications of our work for more general $N = 2$ superconformal field theories.},
doi = {10.1007/JHEP02(2016)159},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2016,
place = {United States},
year = {Wed Feb 24 00:00:00 EST 2016},
month = {Wed Feb 24 00:00:00 EST 2016}
}
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https://doi.org/10.1007/JHEP02(2016)159
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Works referenced in this record:

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

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

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

  • Gaiotto, Davide; Seiberg, Nathan; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2011, Issue 1
  • DOI: 10.1007/JHEP01(2011)078

Schur indices, BPS particles, and Argyres-Douglas theories
journal, January 2016

Wild quiver gauge theories
journal, February 2012

  • Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro
  • Journal of High Energy Physics, Vol. 2012, Issue 2
  • DOI: 10.1007/JHEP02(2012)031

General Argyres-Douglas theory
journal, January 2013

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

Gauge Theories and Macdonald Polynomials
journal, November 2012

  • Gadde, Abhijit; Rastelli, Leonardo; Razamat, Shlomo S.
  • Communications in Mathematical Physics, Vol. 319, Issue 1
  • DOI: 10.1007/s00220-012-1607-8

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

  • Buican, Matthew; Nishinaka, Takahiro; Papageorgakis, Constantinos
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)095

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

Complete graphs, Hilbert series, and the Higgs branch of the 4d <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math> SCFTs
journal, May 2015

Infinite Chiral Symmetry in Four Dimensions
journal, January 2015

  • Beem, Christopher; Lemos, Madalena; Liendo, Pedro
  • Communications in Mathematical Physics, Vol. 336, Issue 3
  • DOI: 10.1007/s00220-014-2272-x

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

  • Buican, Matthew; Giacomelli, Simone; Nishinaka, Takahiro
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)185

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

  • Del Zotto, Michele; Vafa, Cumrun; Xie, Dan
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)123

Higher S-dualities and Shephard-Todd groups
journal, September 2015

  • Cecotti, Sergio; Del Zotto, Michele
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)035

CATEGORICAL TINKERTOYS FOR ${\mathcal N} = 2$ GAUGE THEORIES
journal, March 2013

Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories
journal, December 2012

$ {{\mathcal{W}}_3} $ irregular states and isolated $ \mathcal{N}=2 $ superconformal field theories
journal, March 2013

  • Kanno, Hiroaki; Maruyoshi, Kazunobu; Shiba, Shotaro
  • Journal of High Energy Physics, Vol. 2013, Issue 3
  • DOI: 10.1007/JHEP03(2013)147

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

  • Argyres, Philip C.; Maruyoshi, Kazunobu; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)054

Bootstrapping the superconformal index with surface defects
journal, January 2013

  • Gaiotto, Davide; Rastelli, Leonardo; Razamat, Shlomo S.
  • Journal of High Energy Physics, Vol. 2013, Issue 1
  • DOI: 10.1007/JHEP01(2013)022

Down the rabbit hole with theories of class S $$ \mathcal{S} $$
journal, October 2014

  • Razamat, Shlomo S.; Willett, Brian
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)099

BPS spectrum of Argyres-Douglas theory via spectral network
journal, December 2013

  • Maruyoshi, Kazunobu; Park, Chan Y.; Yan, Wenbin
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)092

Stress-tensor OPE in N = 2 $$ \mathcal{N}=2 $$ superconformal theories
journal, February 2016

  • Liendo, Pedro; Ramírez, Israel; Seo, Jihye
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)019

On renormalization group flows in four dimensions
journal, December 2011

  • Komargodski, Zohar; Schwimmer, Adam
  • Journal of High Energy Physics, Vol. 2011, Issue 12
  • DOI: 10.1007/JHEP12(2011)099

The constraints of conformal symmetry on RG flows
journal, July 2012

IR free or interacting? A proposed diagnostic
journal, December 2005

Non-perturbative constraints on light sparticles from properties of the RG flow
journal, October 2014

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    Works referencing / citing this record:

    On the chiral algebra of Argyres-Douglas theories and S-duality
    journal, April 2018

    • Choi, Jaewang; Nishinaka, Takahiro
    • Journal of High Energy Physics, Vol. 2018, Issue 4
    • DOI: 10.1007/jhep04(2018)004

    Conformal manifolds in four dimensions and chiral algebras
    journal, October 2016

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

    Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
    text, January 2017

    • Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro
    • Deutsches Elektronen-Synchrotron, DESY, Hamburg
    • DOI: 10.3204/pubdb-2017-11690

    Surface Defects and Chiral Algebras
    text, January 2017

    Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
    text, January 2017

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