Superconformal index, BPS monodromy and chiral algebras

Cecotti, Sergio; Song, Jaewon; Vafa, Cumrun; Yan, Wenbin

doi:10.1007/jhep11(2017)013

Title: Superconformal index, BPS monodromy and chiral algebras

Abstract

We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr MN where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras A_N. This generalizes the recent results for the N = –1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S² × T² where we turn on 1/2N units of U(1)_r flux on S².

Authors:

Cecotti, Sergio ^[1]; Song, Jaewon ^[2]; Vafa, Cumrun ^[3]; Yan, Wenbin ^[4]

Scuola Internazionale Superiore di Studi Avanzati, Trieste (Italy)
Univ. of California, La Jolla, CA (United States). Dept. of Physics
Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.
Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab. and Center for Mathematical Sciences and Applications; California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

Publication Date:: Mon Nov 06 00:00:00 EST 2017

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

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

OSTI Identifier:: 1504762

Grant/Contract Number:: SC0009919; PHY-1067976

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: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Supersymmetric Gauge Theory

Citation Formats


                    Cecotti, Sergio, Song, Jaewon, Vafa, Cumrun, and Yan, Wenbin. Superconformal index, BPS monodromy and chiral algebras.  United States: N. p., 2017. 
Web.  doi:10.1007/jhep11(2017)013.

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                    Cecotti, Sergio, Song, Jaewon, Vafa, Cumrun, & Yan, Wenbin. Superconformal index, BPS monodromy and chiral algebras.  United States.  https://doi.org/10.1007/jhep11(2017)013

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                    Cecotti, Sergio, Song, Jaewon, Vafa, Cumrun, and Yan, Wenbin. Mon .  
"Superconformal index, BPS monodromy and chiral algebras".  United States.  https://doi.org/10.1007/jhep11(2017)013.  https://www.osti.gov/servlets/purl/1504762.

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@article{osti_1504762,

  title        = {Superconformal index, BPS monodromy and chiral algebras},

  author       = {Cecotti, Sergio and Song, Jaewon and Vafa, Cumrun and Yan, Wenbin},

  abstractNote = {We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr MN where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras AN. This generalizes the recent results for the N = –1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S2 × T2 where we turn on 1/2N units of U(1)r flux on S2.},

  doi          = {10.1007/jhep11(2017)013},

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

  number       = 11,

  volume       = 2017,

  place        = {United States},

  year         = {Mon Nov 06 00:00:00 EST 2017},

  month        = {Mon Nov 06 00:00:00 EST 2017}

}

Copy to clipboard

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Macdonald index and chiral algebra

Journal Article Song, Jaewon - Journal of High Energy Physics (Online)

For any 4dN = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. Here, we conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A₁, A_2n) and (A₁, D_2n+1) where the chiral algebras are given by Virasoro andmore »« less
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https://doi.org/10.1007/JHEP08(2017)044

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Title: Superconformal index, BPS monodromy and chiral algebras

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The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap journal, March 2016

Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories journal, November 2014

Topological reduction of 4D SYM to 2D σ-models journal, August 1995

BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories journal, August 2013

Topological quantum field theory journal, September 1988

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory journal, July 2010

The Annihilating Ideals of Minimal Models journal, April 1992

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

Gauge Theories and Macdonald Polynomials journal, November 2012

Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT journal, February 2016

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

Abelian current algebra and the Virasoro algebra on the lattice journal, October 1993

Multiple series Rogers-Ramanujan type identities journal, January 1984

Refined, Motivic, and Quantum journal, November 2009

Twistorial topological strings and a $\mathrm{tt}^*$ geometry for $\mathcal{N} = 2$ theories in 4d journal, January 2016

Galois covers of $\mathcal{N}=2$ BPS spectra and quantum monodromy journal, January 2016

Characters of graded parafermion conformal field theory journal, January 2007

An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli journal, October 1974

$\mathcal{N} = 2$ quantum field theories and their BPS quivers journal, January 2014

Dedekind's η-function and Rogers-Ramanujan identities journal, February 2012

Basic hypergeometric series journal, September 1991

Classification of 4d $ \mathcal{N} $ =2 gauge theories journal, December 2013

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups journal, November 2013

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

String Vacua and Orbifoldized lg Models journal, June 1989

Dilogarithm Identities in Conformal Field Theory journal, June 1993

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

On the reduction of 4d N = 1 $$ \mathcal{N}=1 $$ theories on S 2 $$ {\mathbb{S}}^2 $$ journal, November 2015

General Argyres-Douglas theory journal, January 2013

Dyons of charge eθ/2π journal, October 1979

Exceptional vector bundles, tilting sheaves and tilting complexes for weighted projective lines journal, January 2004

Infinite Chiral Symmetry in Four Dimensions journal, January 2015

On classification ofN=2 supersymmetric theories journal, December 1993

Supersymmetric field theories on three-manifolds journal, May 2013

The BPS spectrum of the 4d $ \mathcal{N}=2 $ SCFT’s H 1, H 2, D 4, E 6, E 7, E 8 journal, June 2013

Classification of complete $N = 2$ supersymmetric theories in 4 dimensions journal, January 2013

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

Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories journal, October 2010

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

2d index and surface operators journal, March 2014

Line Operator Index on S 1 × S 3 journal, May 2012

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

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

3-Manifolds and 3d indices journal, January 2013

Variants of the Rogers–Ramanujan Identities journal, October 1999

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

On the conformal field theory of the Higgs branch journal, July 1997

Two-dimensional SCFTs from wrapped branes and c-extremization journal, June 2013

Argyres-Douglas theories, the Macdonald index, and an RG inequality journal, February 2016

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

Y -systems, Q -systems, and 4D $\mathcal {N}=2$ supersymmetric QFT journal, November 2014

On the superconformal index of Argyres–Douglas theories journal, December 2015

On the phase transition towards permanent quark confinement journal, June 1978

A property of electric and magnetic flux in non-Abelian gauge theories journal, January 1979

Topology of the gauge condition and new confinement phases in non-abelian gauge theories journal, October 1981

On Arnold’s 14 ‘exceptional’ $ \mathcal{N} = 2 $ superconformal gauge theories journal, October 2011

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

3-Manifolds and 3d Indices preprint, January 2011

Supersymmetric Field Theories on Three-Manifolds text, January 2012

2d Index and Surface operators text, January 2013

Infinite Chiral Symmetry in Four Dimensions text, January 2013

A topologically twisted index for three-dimensional supersymmetric theories text, January 2015

On the Superconformal Index of Argyres-Douglas Theories text, January 2015

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

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

Characters of graded parafermion conformal field theory preprint, January 2006

Abelian Current Algebra and the Virasoro Algebra on the Lattice text, January 1993

On The Conformal Field Theory Of The Higgs Branch text, January 1997

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

Quantum Wall Crossing in N=2 Gauge Theories text, January 2009

Higher S-dualities and Shephard-Todd groups preprint, January 2015

Vertex operator algebras of Argyres-Douglas theories from M5-branes journal, December 2017

Hidden exceptional symmetry in the pure spinor superstring journal, January 2020

TBA equations and resurgent Quantum Mechanics journal, January 2019

Vertex operator algebras, Higgs branches, and modular differential equations journal, August 2018

Four-dimensional lens space index from two-dimensional chiral algebra journal, July 2018

(0,4) dualities
journal, March 2016

The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap
journal, March 2016

Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories
journal, November 2014

Topological reduction of 4D SYM to 2D σ-models
journal, August 1995

BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories
journal, August 2013

Topological quantum field theory
journal, September 1988

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010

The Annihilating Ideals of Minimal Models
journal, April 1992

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

Gauge Theories and Macdonald Polynomials
journal, November 2012

Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
journal, February 2016

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

Abelian current algebra and the Virasoro algebra on the lattice
journal, October 1993

Multiple series Rogers-Ramanujan type identities
journal, January 1984

Refined, Motivic, and Quantum
journal, November 2009

Twistorial topological strings and a $\mathrm{tt}^*$ geometry for $\mathcal{N} = 2$ theories in 4d
journal, January 2016

Galois covers of $\mathcal{N}=2$ BPS spectra and quantum monodromy
journal, January 2016

Characters of graded parafermion conformal field theory
journal, January 2007

An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli
journal, October 1974

$\mathcal{N} = 2$ quantum field theories and their BPS quivers
journal, January 2014

Dedekind's η-function and Rogers-Ramanujan identities
journal, February 2012

Basic hypergeometric series
journal, September 1991

Classification of 4d $ \mathcal{N} $ =2 gauge theories
journal, December 2013

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups
journal, November 2013

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

String Vacua and Orbifoldized lg Models
journal, June 1989

Dilogarithm Identities in Conformal Field Theory
journal, June 1993

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

On the reduction of 4d N = 1 $$ \mathcal{N}=1 $$ theories on S 2 $$ {\mathbb{S}}^2 $$
journal, November 2015

General Argyres-Douglas theory
journal, January 2013

Dyons of charge eθ/2π
journal, October 1979

Exceptional vector bundles, tilting sheaves and tilting complexes for weighted projective lines
journal, January 2004

Infinite Chiral Symmetry in Four Dimensions
journal, January 2015

On classification ofN=2 supersymmetric theories
journal, December 1993

Supersymmetric field theories on three-manifolds
journal, May 2013

The BPS spectrum of the 4d $ \mathcal{N}=2 $ SCFT’s H 1, H 2, D 4, E 6, E 7, E 8
journal, June 2013

Classification of complete $N = 2$ supersymmetric theories in 4 dimensions
journal, January 2013

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

Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories
journal, October 2010

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

2d index and surface operators
journal, March 2014

Line Operator Index on S 1 × S 3
journal, May 2012

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

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

3-Manifolds and 3d indices
journal, January 2013

Variants of the Rogers–Ramanujan Identities
journal, October 1999

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

On the conformal field theory of the Higgs branch
journal, July 1997

Two-dimensional SCFTs from wrapped branes and c-extremization
journal, June 2013

Argyres-Douglas theories, the Macdonald index, and an RG inequality
journal, February 2016

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

Y -systems, Q -systems, and 4D $\mathcal {N}=2$ supersymmetric QFT
journal, November 2014

On the superconformal index of Argyres–Douglas theories
journal, December 2015

On the phase transition towards permanent quark confinement
journal, June 1978

A property of electric and magnetic flux in non-Abelian gauge theories
journal, January 1979

Topology of the gauge condition and new confinement phases in non-abelian gauge theories
journal, October 1981

On Arnold’s 14 ‘exceptional’ $ \mathcal{N} = 2 $ superconformal gauge theories
journal, October 2011

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

3-Manifolds and 3d Indices
preprint, January 2011

Supersymmetric Field Theories on Three-Manifolds
text, January 2012

2d Index and Surface operators
text, January 2013

Infinite Chiral Symmetry in Four Dimensions
text, January 2013

A topologically twisted index for three-dimensional supersymmetric theories
text, January 2015

On the Superconformal Index of Argyres-Douglas Theories
text, January 2015

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

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

Characters of graded parafermion conformal field theory
preprint, January 2006

Abelian Current Algebra and the Virasoro Algebra on the Lattice
text, January 1993

On The Conformal Field Theory Of The Higgs Branch
text, January 1997

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

Quantum Wall Crossing in N=2 Gauge Theories
text, January 2009

Higher S-dualities and Shephard-Todd groups
preprint, January 2015

Vertex operator algebras of Argyres-Douglas theories from M5-branes
journal, December 2017

Hidden exceptional symmetry in the pure spinor superstring
journal, January 2020

TBA equations and resurgent Quantum Mechanics
journal, January 2019

Vertex operator algebras, Higgs branches, and modular differential equations
journal, August 2018

Four-dimensional lens space index from two-dimensional chiral algebra
journal, July 2018

Vanishing OPE coefficients in 4d $$ \mathcal{N}=2 $$ SCFTs
journal, June 2019

Universal features of BPS strings in six-dimensional SCFTs
journal, August 2018

Universal RG flows across dimensions and holography
journal, December 2017