Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT

Song, Jaewon

doi:10.1007/JHEP02(2016)045

Title: Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT

Abstract

We present superconformal indices of 4d N = 2 class S theories with certain irregular punctures called type I_k,N. This class of theories include generalized Argyres-Douglas theories of type (A_k-1, A_N-1) and more. We conjecture the superconformal indices in certain simplifi ed limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture I_k,N. We write the Schur limit of the wave function when k and N are coprime. When k = 2, we also conjecture a closed-form expression for the Hall-Littlewood index and the Macdonald index for odd N. From the index, we argue that certain short-multiplet which can appear in the OPE of the stress-energy tensor is absent in the (A₁,A_2n) theory. In addition, we discuss the mixed Schur indices for the N = 1 class S theories with irregular punctures.

Authors:

Song, Jaewon ^[1]

Univ. of California, San Diego, CA (United States). Department of Physics

Publication Date:: Fri Feb 05 00:00:00 EST 2016

Research Org.:: Univ. of California, San Diego, CA (United States)

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

OSTI Identifier:: 1327262

Grant/Contract Number:: SC0009919

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:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Supersymmetric gauge theory; Supersymmetry and Duality; Topological Field Theories

Citation Formats


                    Song, Jaewon. Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP02(2016)045.

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                    Song, Jaewon. Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT.  United States.  https://doi.org/10.1007/JHEP02(2016)045

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                    Song, Jaewon. Fri .  
"Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT".  United States.  https://doi.org/10.1007/JHEP02(2016)045.  https://www.osti.gov/servlets/purl/1327262.

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@article{osti_1327262,

  title        = {Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT},

  author       = {Song, Jaewon},

  abstractNote = {We present superconformal indices of 4d N = 2 class S theories with certain irregular punctures called type Ik,N. This class of theories include generalized Argyres-Douglas theories of type (Ak-1, AN-1) and more. We conjecture the superconformal indices in certain simplifi ed limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture Ik,N. We write the Schur limit of the wave function when k and N are coprime. When k = 2, we also conjecture a closed-form expression for the Hall-Littlewood index and the Macdonald index for odd N. From the index, we argue that certain short-multiplet which can appear in the OPE of the stress-energy tensor is absent in the (A1,A2n) theory. In addition, we discuss the mixed Schur indices for the N = 1 class S theories with irregular punctures.},

  doi          = {10.1007/JHEP02(2016)045},

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

  number       = 2,

  volume       = 2016,

  place        = {United States},

  year         = {Fri Feb 05 00:00:00 EST 2016},

  month        = {Fri Feb 05 00:00:00 EST 2016}

}

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Journal Article Dedushenko, Mykola ; Gukov, Sergei ; Nakajima, Hiraku ; ... - Journal of Physics. A, Mathematical and Theoretical

We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres–Douglas theories on S¹ × M³ with a non-trivial holonomy of a discrete global symmetry along the S¹. For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern–Simons and Rozansky–Witten types respectively. Changing the holonomy performs a Galois transformation on the TQFT, which can sometimes give rise to more familiar unitary theories such as themore »« less
https://doi.org/10.1088/1751-8121/abb481

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Equivariant Verlinde Algebra from Superconformal Index and Argyres–Seiberg Duality

Journal Article Gukov, Sergei ; Pei, Du ; Yan, Wenbin ; ... - Communications in Mathematical Physics

Here, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the “Coulomb branch index” of the class ${{\mathcal S}}$ theory ${T[\Sigma,G]}$ on ${L(k,1) \times S^1}$, the other is the ${^L G}$ “equivariant Verlinde formula”, or equivalently partition function of ${^L G_{\mathbb{C}}}$ complex Chern–Simons theory on ${\Sigma\times S^1}$. We first derive this equivalence using the M-theory geometry and show that the gauge groups appearing on the two sides are naturally G and its Langlands dual ${^L G}$. When G is not simply-connected, we provide a recipe of computing the index of ${T[\Sigma,G]}$ as summation over the indicesmore »« less
Cited by 8
https://doi.org/10.1007/s00220-017-3074-8

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

Journal Article Buican, Matthew ; Nishinaka, Takahiro - Journal of Physics. A, Mathematical and Theoretical

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 Rmore »« less
Cited by 38
https://doi.org/10.1088/1751-8113/49/4/045401

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Title: Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT

Abstract

Citation Formats

N = 2 dualities journal, August 2012

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

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

S-duality and 2d topological QFT journal, March 2010

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

Gauge Theories and Macdonald Polynomials journal, November 2012

Bootstrapping the superconformal index with surface defects journal, January 2013

Black holes, q-deformed 2d Yang–Mills, and non-perturbative topological strings journal, May 2005

5D SYM on 3D sphere and 2D YM journal, October 2012

5D SYM and 2D q-deformed YM journal, April 2013

5D SYM on 3D deformed spheres journal, September 2015

On S-duality of the superconformal index on lens spaces and 2d TQFT journal, May 2013

S-duality and the $ \mathcal{N}=2 $ lens space index journal, October 2013

2d TQFT structure of the superconformal indices with outer-automorphism twists journal, March 2013

The superconformal index of class $ \mathcal{S} $ theories of type D journal, May 2014

Tinkertoys for the twisted D-series journal, April 2015

New N = 1 dualities from M5-branes and outer-automorphism twists journal, March 2014

Tinkertoys for the E 6 theory journal, September 2015

General Argyres-Douglas theory journal, January 2013

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

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

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

Infinite Chiral Symmetry in Four Dimensions journal, January 2015

Chiral algebras of class S $$ \mathcal{S} $$ journal, May 2015

Chiral algebras for trinion theories journal, February 2015

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

Sicilian gauge theories and $$ \mathcal{N} $$ = 1 dualities journal, January 2010

Four-dimensional SCFTs from M5-branes journal, June 2012

The $ \mathcal{N} $ = 1 superconformal index for class $ \mathcal{S} $ fixed points journal, April 2014

M5 brane and four dimensional $ \mathcal{N} $ = 1 theories I journal, April 2014

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

Asymptotically free = 2 theories and irregular conformal blocks journal, December 2013

On AGT conjecture for pure super Yang-Mills and W-algebra journal, May 2011

The ABCDEFG of instantons and W-algebras journal, March 2012

Liouville Correlation Functions from Four-Dimensional Gauge Theories journal, January 2010

A N −1 conformal Toda field theory correlation functions from conformal 𝒩 = 2 SU( N ) quiver gauge theories journal, November 2009

Wild quiver gauge theories journal, February 2012

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

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

Mirror symmetry in three dimensional gauge theories journal, October 1996

Monopole operators and Hilbert series of Coulomb branches of 3d $ \mathcal{N} $ = 4 gauge theories journal, January 2014

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

$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory journal, January 2009

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

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

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

Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators journal, January 2016

New $ \mathcal{N} $ =1 dualities journal, June 2013

Quiver tails and N = 1 $$ \mathcal{N}=1 $$ SCFTs from M5-branes journal, March 2015

Infinitely many N = 1 $$ \mathcal{N}=1 $$ dualities from m + 1 − m = 1 journal, October 2015

Vanishing superconformal indices and the chiral symmetry breaking journal, June 2014

Generalized Hitchin system, spectral curve and $ \mathcal{N} $ =1 dynamics journal, January 2014

Central charges of N=2 superconformal field theories in four dimensions text, January 2008

Liouville Correlation Functions from Four-dimensional Gauge Theories text, January 2009

S-duality and 2d Topological QFT text, January 2009

On AGT Conjecture for Pure Super Yang-Mills and W-algebra text, January 2009

Four-Dimensional SCFTs from M5-Branes text, January 2012

Bootstrapping the superconformal index with surface defects text, January 2012

On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT text, January 2013

Tinkertoys for the Twisted D-Series preprint, January 2013

Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories text, January 2013

New N=1 Dualities from M5-branes and Outer-automorphism Twists text, January 2013

Infinite Chiral Symmetry in Four Dimensions text, January 2013

Tinkertoys for the $E_6$ Theory preprint, January 2014

Complete Graphs, Hilbert Series, and the Higgs branch of the 4d N=2 $(A_n,A_m)$ SCFT's text, January 2014

5D SYM on 3D Deformed Spheres text, January 2015

Schur Indices, BPS Particles, and Argyres-Douglas Theories text, January 2015

On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry text, January 2002

Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings text, January 2004

An Index for 4 dimensional Super Conformal Theories text, January 2005

New N=2 Superconformal Field Theories in Four Dimensions text, January 1995

Mirror Symmetry in Three Dimensional Gauge Theories text, January 1996

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

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

Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6D (2,0) theories journal, July 2019

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

N = 2 dualities
journal, August 2012

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

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

S-duality and 2d topological QFT
journal, March 2010

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

Gauge Theories and Macdonald Polynomials
journal, November 2012

Bootstrapping the superconformal index with surface defects
journal, January 2013

Black holes, q-deformed 2d Yang–Mills, and non-perturbative topological strings
journal, May 2005

5D SYM on 3D sphere and 2D YM
journal, October 2012

5D SYM and 2D q-deformed YM
journal, April 2013

5D SYM on 3D deformed spheres
journal, September 2015

On S-duality of the superconformal index on lens spaces and 2d TQFT
journal, May 2013

S-duality and the $ \mathcal{N}=2 $ lens space index
journal, October 2013

2d TQFT structure of the superconformal indices with outer-automorphism twists
journal, March 2013

The superconformal index of class $ \mathcal{S} $ theories of type D
journal, May 2014

Tinkertoys for the twisted D-series
journal, April 2015

New N = 1 dualities from M5-branes and outer-automorphism twists
journal, March 2014

Tinkertoys for the E 6 theory
journal, September 2015

General Argyres-Douglas theory
journal, January 2013

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

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

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

Infinite Chiral Symmetry in Four Dimensions
journal, January 2015

Chiral algebras of class S $$ \mathcal{S} $$
journal, May 2015

Chiral algebras for trinion theories
journal, February 2015

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

Sicilian gauge theories and $$ \mathcal{N} $$ = 1 dualities
journal, January 2010

Four-dimensional SCFTs from M5-branes
journal, June 2012

The $ \mathcal{N} $ = 1 superconformal index for class $ \mathcal{S} $ fixed points
journal, April 2014

M5 brane and four dimensional $ \mathcal{N} $ = 1 theories I
journal, April 2014

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

Asymptotically free = 2 theories and irregular conformal blocks
journal, December 2013

On AGT conjecture for pure super Yang-Mills and W-algebra
journal, May 2011

The ABCDEFG of instantons and W-algebras
journal, March 2012

Liouville Correlation Functions from Four-Dimensional Gauge Theories
journal, January 2010

A _{N −1} conformal Toda field theory correlation functions from conformal 𝒩 = 2 SU( N ) quiver gauge theories
journal, November 2009

Wild quiver gauge theories
journal, February 2012

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

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

Mirror symmetry in three dimensional gauge theories
journal, October 1996

Monopole operators and Hilbert series of Coulomb branches of 3d $ \mathcal{N} $ = 4 gauge theories
journal, January 2014

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

$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory
journal, January 2009

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

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

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

Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators
journal, January 2016

New $ \mathcal{N} $ =1 dualities
journal, June 2013

Quiver tails and N = 1 $$ \mathcal{N}=1 $$ SCFTs from M5-branes
journal, March 2015

Infinitely many N = 1 $$ \mathcal{N}=1 $$ dualities from m + 1 − m = 1
journal, October 2015

Vanishing superconformal indices and the chiral symmetry breaking
journal, June 2014

Generalized Hitchin system, spectral curve and $ \mathcal{N} $ =1 dynamics
journal, January 2014

Central charges of N=2 superconformal field theories in four dimensions
text, January 2008

Liouville Correlation Functions from Four-dimensional Gauge Theories
text, January 2009

S-duality and 2d Topological QFT
text, January 2009

On AGT Conjecture for Pure Super Yang-Mills and W-algebra
text, January 2009

Four-Dimensional SCFTs from M5-Branes
text, January 2012

Bootstrapping the superconformal index with surface defects
text, January 2012

On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT
text, January 2013

Tinkertoys for the Twisted D-Series
preprint, January 2013

Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
text, January 2013

New N=1 Dualities from M5-branes and Outer-automorphism Twists
text, January 2013

Infinite Chiral Symmetry in Four Dimensions
text, January 2013

Tinkertoys for the $E_6$ Theory
preprint, January 2014

Complete Graphs, Hilbert Series, and the Higgs branch of the 4d N=2 $(A_n,A_m)$ SCFT's
text, January 2014

5D SYM on 3D Deformed Spheres
text, January 2015

Schur Indices, BPS Particles, and Argyres-Douglas Theories
text, January 2015

On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
text, January 2002

Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
text, January 2004

An Index for 4 dimensional Super Conformal Theories
text, January 2005

New N=2 Superconformal Field Theories in Four Dimensions
text, January 1995

Mirror Symmetry in Three Dimensional Gauge Theories
text, January 1996

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

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

Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6D (2,0) theories
journal, July 2019

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

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

Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
text, January 2016

Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
text, January 2017