Four-dimensional lens space index from two-dimensional chiral algebra

Fluder, Martin; Song, Jaewon

doi:10.1007/jhep07(2018)073

Title: Four-dimensional lens space index from two-dimensional chiral algebra

Abstract

We study the supersymmetric partition function on S¹ × L(r, 1), or the lens space index of four-dimensional N = 2 superconformal field theories and their connection to two-dimensional chiral algebras. We primarily focus on free theories as well as ArgyresDouglas theories of type (A₁, A_k) and (A₁, D_k). We observe that in specific limits, the lens space index is reproduced in terms of the (refined) character of an appropriately twisted module of the associated two-dimensional chiral algebra or a generalized vertex operator algebra. In conclusion the particular twisted module is determined by the choice of discrete holonomies for the flavor symmetry in four-dimensions.

Authors:

Fluder, Martin ^[1];

^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Korea Inst. for Advanced Study, Seoul (Korea); Univ. of California, San Diego, CA (United States). Dept. of Physics

Publication Date:: Wed Jul 11 00:00:00 EDT 2018

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1501463

Grant/Contract Number:: SC0011632

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: 2018; Journal Issue: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Conformal Field Theory; Extended Supersymmetry; Supersymmetric Gauge Theory

Citation Formats


                    Fluder, Martin, and Song, Jaewon. Four-dimensional lens space index from two-dimensional chiral algebra.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep07(2018)073.

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                    Fluder, Martin, & Song, Jaewon. Four-dimensional lens space index from two-dimensional chiral algebra.  United States.  https://doi.org/10.1007/jhep07(2018)073

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                    Fluder, Martin, and Song, Jaewon. Wed .  
"Four-dimensional lens space index from two-dimensional chiral algebra".  United States.  https://doi.org/10.1007/jhep07(2018)073.  https://www.osti.gov/servlets/purl/1501463.

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@article{osti_1501463,

  title        = {Four-dimensional lens space index from two-dimensional chiral algebra},

  author       = {Fluder, Martin and Song, Jaewon},

  abstractNote = {We study the supersymmetric partition function on S1 × L(r, 1), or the lens space index of four-dimensional N = 2 superconformal field theories and their connection to two-dimensional chiral algebras. We primarily focus on free theories as well as ArgyresDouglas theories of type (A1, Ak) and (A1, Dk). We observe that in specific limits, the lens space index is reproduced in terms of the (refined) character of an appropriately twisted module of the associated two-dimensional chiral algebra or a generalized vertex operator algebra. In conclusion the particular twisted module is determined by the choice of discrete holonomies for the flavor symmetry in four-dimensions.},

  doi          = {10.1007/jhep07(2018)073},

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

  number       = 7,

  volume       = 2018,

  place        = {United States},

  year         = {Wed Jul 11 00:00:00 EDT 2018},

  month        = {Wed Jul 11 00:00:00 EDT 2018}

}

Copy to clipboard

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Works referencing / citing this record:

Vanishing OPE coefficients in 4d $$ \mathcal{N}=2 $$ SCFTs
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Dedushenko, Mykola; Wang, Yifan
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Title: Four-dimensional lens space index from two-dimensional chiral algebra

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Abelianizing Vertex Algebras journal, April 2005

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

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

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

4d index to 3d index and 2d topological quantum field theory journal, September 2012

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

Study of $N=2$ Superconformal Field Theories in $4$ Dimensions text, January 1996

Studying superconformal symmetry enhancement through indices text, January 2017

Ghost systems: a vertex algebra point of view journal, May 1998

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

Line defect Schur indices, Verlinde algebras and U(1)r fixed points journal, November 2017

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

General Argyres-Douglas theory journal, January 2013

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Infinite Chiral Symmetry in Four Dimensions journal, January 2015

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

Infinite Chiral Symmetry in Four Dimensions text, January 2013

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

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

N $$ \mathcal{N} $$ =1 Lagrangians for generalized Argyres-Douglas theories journal, October 2017

Abelianization and sequential confinement in 2 + 1 dimensions journal, October 2017

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

Macdonald index and chiral algebra journal, August 2017

W $$ \mathcal{W} $$ symmetry in six dimensions journal, May 2015

Surface defects and chiral algebras journal, May 2017

Chiral algebras for trinion theories journal, February 2015

The PBW filtration journal, May 2009

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

Ghost Systems: A Vertex Algebra Point of View text, January 1997

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

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

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Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality text, January 2016

Superconformal index, BPS monodromy and chiral algebras journal, November 2017

N $$ \mathcal{N} $$ =1 Deformations and RG flows of N $$ \mathcal{N} $$ =2 SCFTs, part II: non-principal deformations journal, December 2016

Studying superconformal symmetry enhancement through indices journal, April 2018

Global Properties of Supersymmetric Theories and the Lens Space journal, July 2014

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

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N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs journal, February 2017

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Equivariant Verlinde Algebra from Superconformal Index and Argyres–Seiberg Duality
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Supersymmetric Gauge Theories with Decoupled Operators and Chiral Ring Stability
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Abelianizing Vertex Algebras
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On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT
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text, January 1996

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text, January 2017

Ghost systems: a vertex algebra point of view
journal, May 1998

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Stress-tensor OPE in N = 2 $$ \mathcal{N}=2 $$ superconformal theories
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journal, October 2017

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journal, December 2002

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journal, January 2015

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text, January 2016

Infinite Chiral Symmetry in Four Dimensions
text, January 2013

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journal, July 1996

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

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journal, October 2017

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text, January 1995

Macdonald index and chiral algebra
journal, August 2017

W $$ \mathcal{W} $$ symmetry in six dimensions
journal, May 2015

Surface defects and chiral algebras
journal, May 2017

Chiral algebras for trinion theories
journal, February 2015

The PBW filtration
journal, May 2009

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

Ghost Systems: A Vertex Algebra Point of View
text, January 1997

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

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

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

Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
text, January 2016

Superconformal index, BPS monodromy and chiral algebras
journal, November 2017

N $$ \mathcal{N} $$ =1 Deformations and RG flows of N $$ \mathcal{N} $$ =2 SCFTs, part II: non-principal deformations
journal, December 2016

Studying superconformal symmetry enhancement through indices
journal, April 2018

Global Properties of Supersymmetric Theories and the Lens Space
journal, July 2014

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

N = 2 $$ \mathcal{N}=2 $$ central charge bounds from 2d chiral algebras
journal, April 2016

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, February 2017

Surface defect indices and 2d-4d BPS states
journal, December 2017

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

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

Logarithmic W-algebras and Argyres-Douglas theories at higher rank
journal, November 2018

IR duality in 2D $N = (0, 2)$ gauge theory with noncompact dynamics
journal, March 2019

Testing Macdonald index as a refined character of chiral algebra
journal, February 2020

Chiral algebra, localization, modularity, surface defects, and all that
journal, September 2020

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
text, January 2018

OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
text, January 2018

4d/2d $\rightarrow $ 3d/1d: A song of protected operator algebras
preprint, January 2019