The supersymmetric affine Yangian

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

doi:10.1007/jhep05(2018)200

Title: The supersymmetric affine Yangian

Journal Article · Wed May 30 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep05(2018)200· OSTI ID:1502090

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

Eidgenössische Technische Hochschule (ETH), Zürich (Switzerland). Inst. for Theoretical Physics
Chinese Academy of Sciences (CAS), Beijing (China). Inst. of Theoretical Physics
Brown Univ., Providence, RI (United States). Dept. of Physics

The affine Yangian of gl₁ is known to be isomorphic to W_1+∞, the W-algebra that characterizes the bosonic higher spin — CFT duality. In this paper we propose some of the defining relations of the Yangian that are relevant for the N = 2 superconformal version of W_1+∞. Our construction is based on the observation that the N = 2 superconformal W_1+∞ algebra contains two commuting bosonic W_1+∞ algebras, and that the additional generators transform in bi-minimal representations with respect to these two algebras. As a result, the corresponding affine Yangian can therefore be built up from two affine Yangians of gl₁ by adding in generators that transform appropriately.

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0010010

OSTI ID:: 1502090

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 5; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 25 works

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Gluing two affine Yangians of 𝔤𝔩1 Li, Wei; Longhi, Pietro Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)131	journal	October 2019
Webs of W-algebras Procházka, Tomáš; Rapčák, Miroslav Journal of High Energy Physics, Vol. 2018, Issue 11 https://doi.org/10.1007/jhep11(2018)109	journal	November 2018
Twin-plane-partitions and N $$ \mathcal{N} $$ = 2 affine Yangian Gaberdiel, Matthias R.; Li, Wei; Peng, Cheng Journal of High Energy Physics, Vol. 2018, Issue 11 https://doi.org/10.1007/jhep11(2018)192	journal	November 2018
The matrix-extended $$ {\mathcal{W}}_{1+\infty } $$ algebra Eberhardt, Lorenz; Procházka, Tomáš Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/jhep12(2019)175	journal	December 2019
Rectangular $W$ algebras and superalgebras and their representations Creutzig, Thomas; Hikida, Yasuaki Physical Review D, Vol. 100, Issue 8 https://doi.org/10.1103/physrevd.100.086008	journal	October 2019
Gluing two affine Yangians of gl(1) Li, Wei; Longhi, Pietro ETH Zurich https://doi.org/10.3929/ethz-b-000373045	text	January 2019
Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian Gaberdiel, Matthias R.; Li, Wei; Peng, Cheng arXiv https://doi.org/10.48550/arxiv.1807.11304	text	January 2018

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