Twin-plane-partitions and $\mathcal{N}$ = 2 affine Yangian

Gaberdiel, Matthias R.; Li, Wei; Peng, Cheng

doi:10.1007/jhep11(2018)192

Title: Twin-plane-partitions and $$\mathcal{N}$$ = 2 affine Yangian

Abstract

The universal enveloping algebra of W_1+∞ is isomorphic to the affine Yangian of $$\mathfrak{g}{\mathfrak{l}}_1$$. We study the N = 2 supersymmetric version of this correspondence, and identify the full set of defining relations of the supersymmetric affine Yangian. These relations can be deduced by demanding that the algebra has a representation on twin-plane-partitions, which we construct by gluing pairs of plane partitions. We define the action of the algebra on these twin-plane-partitions explicitly

Authors:

Gaberdiel, Matthias R. ^[1]; Li, Wei ^[2]; Peng, Cheng ^[3]

ETH, Zurich (Switzerland)
Chinese Academy of Science (CAS), Beijing (China)
Brown Univ., Providence, RI (United States)

Publication Date:: Thu Nov 29 00:00:00 EST 2018

Research Org.:: Brown Univ., Providence, RI (United States)

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

OSTI Identifier:: 1611327

Grant/Contract Number:: SC0010010

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: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; physics; conformal and W symmetry; extended supersymmetry; higher spin symmetry; quantum groups

Citation Formats


                    Gaberdiel, Matthias R., Li, Wei, and Peng, Cheng. Twin-plane-partitions and $\mathcal{N}$ = 2 affine Yangian.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep11(2018)192.

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                    Gaberdiel, Matthias R., Li, Wei, & Peng, Cheng. Twin-plane-partitions and $\mathcal{N}$ = 2 affine Yangian.  United States.  https://doi.org/10.1007/jhep11(2018)192

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                    Gaberdiel, Matthias R., Li, Wei, and Peng, Cheng. Thu .  
"Twin-plane-partitions and $\mathcal{N}$ = 2 affine Yangian".  United States.  https://doi.org/10.1007/jhep11(2018)192.  https://www.osti.gov/servlets/purl/1611327.

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@article{osti_1611327,

  title        = {Twin-plane-partitions and $\mathcal{N}$ = 2 affine Yangian},

  author       = {Gaberdiel, Matthias R. and Li, Wei and Peng, Cheng},

  abstractNote = {The universal enveloping algebra of W1+∞ is isomorphic to the affine Yangian of $\mathfrak{g}{\mathfrak{l}}_1$. We study the N = 2 supersymmetric version of this correspondence, and identify the full set of defining relations of the supersymmetric affine Yangian. These relations can be deduced by demanding that the algebra has a representation on twin-plane-partitions, which we construct by gluing pairs of plane partitions. We define the action of the algebra on these twin-plane-partitions explicitly},

  doi          = {10.1007/jhep11(2018)192},

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

  number       = 11,

  volume       = 2018,

  place        = {United States},

  year         = {Thu Nov 29 00:00:00 EST 2018},

  month        = {Thu Nov 29 00:00:00 EST 2018}

}

Copy to clipboard

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Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
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Duality in $ \mathcal{N}=2 $ minimal model holography
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Higher spins on AdS3 from the worldsheet
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Ferreira, Kevin; Gaberdiel, Matthias R.; Jottar, Juan I.
ETH Zurich
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Tensionless string spectra on AdS(3)
text, January 2018

Gaberdiel, Matthias R.; Gopakumar, Rajesh
ETH Zurich
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The supersymmetric affine Yangian
text, January 2018

Gaberdiel, Matthias R.; Li, Wei; Peng, Cheng
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Works referencing / citing this record:

The matrix-extended $$ {\mathcal{W}}_{1+\infty } $$ algebra
journal, December 2019

Eberhardt, Lorenz; Procházka, Tomáš
Journal of High Energy Physics, Vol. 2019, Issue 12
DOI: 10.1007/jhep12(2019)175

Rectangular W-algebras, extended higher spin gravity and dual coset CFTs
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Creutzig, Thomas; Hikida, Yasuaki
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Gluing two affine Yangians of 𝔤𝔩1
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Li, Wei; Longhi, Pietro
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Gluing two affine Yangians of gl(1)
text, January 2019

Li, Wei; Longhi, Pietro
ETH Zurich
DOI: 10.3929/ethz-b-000373045

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Title: Twin-plane-partitions and $$\mathcal{N}$$ = 2 affine Yangian

Abstract

Citation Formats

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity journal, January 2013

Perturbations of $ \mathcal{W} $ ∞ CFTs journal, October 2013

Stringy AdS(3) from the worldsheet text, January 2017

W $$ \mathcal{W} $$ -symmetry, topological vertex and affine Yangian journal, October 2016

Quantum toroidal $\mathfrak{gl}_{1}$ -algebra: Plane partitions journal, January 2012

Quantum continuous $\mathfrak{gl}_{\infty}$ : Semiinfinite construction of representations journal, January 2011

Tensionless string spectra on AdS3 journal, May 2018

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Stringy gravity, interacting tensionless strings and massless higher spins journal, September 2001

Nonlinear equations for symmetric massless higher spin fields in (A)dSd journal, August 2003

Quasifinite highest weight modules over the superW 1+∞algebra journal, May 1995

Triality in minimal model holography journal, July 2012

A (q,γ) analog of the W1+∞ algebra journal, December 2007

Review of AdS/CFT Integrability: An Overview journal, October 2011

Higher spins and Yangian symmetries text, January 2017

The affine Yangian of gl 1 revisited journal, January 2017

Stringy AdS3 from the worldsheet journal, July 2017

Quantum continuous gl∞: Tensor products of Fock modules and Wn-characters journal, January 2011

Nonlinear W∞ as asymptotic symmetry of three-dimensional higher spin AdS gravity journal, December 2010

Higher spins and Yangian symmetries journal, April 2017

Higher spins on AdS3 from the worldsheet journal, July 2017

Twisted sectors from plane partitions journal, September 2016

Yangian associated with 2D 𝒩 = 1 SCFT journal, September 2015

Superstrings on AdS3 at k = 1 journal, August 2018

The N = 2 super-W3 algebra journal, January 1992

The supersymmetric affine Yangian journal, May 2018

Higher spins & strings text, January 2014

Higher spins & strings journal, November 2014

Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields journal, November 2010

Twisted sectors from plane partitions text, January 2016

Duality in $ \mathcal{N}=2 $ minimal model holography journal, February 2013

Higher spins on AdS3 from the worldsheet text, January 2017

Tensionless string spectra on AdS(3) text, January 2018

The supersymmetric affine Yangian text, January 2018

Review of AdS/CFT Integrability: An Overview text, January 2010

Triality in Minimal Model Holography text, January 2012

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity text, January 2012

Higher Spins & Strings text, January 2014

Twisted sectors from plane partitions text, January 2016

Stringy AdS3 from the Worldsheet text, January 2017

Stringy gravity, interacting tensionless strings and massless higher spins text, January 2001

Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)dS_d$ text, January 2003

Stringy Symmetries and the Higher Spin Square preprint, January 2015

The matrix-extended $$ {\mathcal{W}}_{1+\infty } $$ algebra journal, December 2019

Rectangular W-algebras, extended higher spin gravity and dual coset CFTs journal, February 2019

Rectangular W algebras and superalgebras and their representations journal, October 2019

Gluing two affine Yangians of 𝔤𝔩1 journal, October 2019

Gluing two affine Yangians of gl(1) text, January 2019

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity
journal, January 2013

Perturbations of $ \mathcal{W} $ ∞ CFTs
journal, October 2013

Stringy AdS(3) from the worldsheet
text, January 2017

W $$ \mathcal{W} $$ -symmetry, topological vertex and affine Yangian
journal, October 2016

Quantum toroidal $\mathfrak{gl}_{1}$ -algebra: Plane partitions
journal, January 2012

Quantum continuous $\mathfrak{gl}_{\infty}$ : Semiinfinite construction of representations
journal, January 2011

Tensionless string spectra on AdS3
journal, May 2018

Triality in minimal model holography
text, January 2012

Stringy gravity, interacting tensionless strings and massless higher spins
journal, September 2001

Nonlinear equations for symmetric massless higher spin fields in (A)dSd
journal, August 2003

Quasifinite highest weight modules over the superW 1+∞algebra
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Triality in minimal model holography
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A (q,γ) analog of the W1+∞ algebra
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Review of AdS/CFT Integrability: An Overview
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Higher spins and Yangian symmetries
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The affine Yangian of ${gl}_{1}$ revisited
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Stringy AdS3 from the worldsheet
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Quantum continuous gl∞: Tensor products of Fock modules and Wn-characters
journal, January 2011

Nonlinear W∞ as asymptotic symmetry of three-dimensional higher spin AdS gravity
journal, December 2010

Higher spins and Yangian symmetries
journal, April 2017

Higher spins on AdS3 from the worldsheet
journal, July 2017

Twisted sectors from plane partitions
journal, September 2016

Yangian associated with 2D 𝒩 = 1 SCFT
journal, September 2015

Superstrings on AdS3 at k = 1
journal, August 2018

The N = 2 super-W3 algebra
journal, January 1992

The supersymmetric affine Yangian
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Higher spins & strings
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Higher spins & strings
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Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
journal, November 2010

Twisted sectors from plane partitions
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Duality in $ \mathcal{N}=2 $ minimal model holography
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Higher spins on AdS3 from the worldsheet
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Tensionless string spectra on AdS(3)
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The supersymmetric affine Yangian
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Review of AdS/CFT Integrability: An Overview
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Triality in Minimal Model Holography
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Supersymmetry of classical solutions in Chern-Simons higher spin supergravity
text, January 2012

Higher Spins & Strings
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Twisted sectors from plane partitions
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Stringy AdS3 from the Worldsheet
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Stringy gravity, interacting tensionless strings and massless higher spins
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Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)dS_d$
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