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Higher spins and Yangian symmetries

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [4]
  1. Federal Inst. of Technology, Zurich (Switzerland). Inst. fur Theoretische Physik; Brown University
  2. International Centre for Theoretical Sciences-TIFR, Bengaluru (India)
  3. Chinese Academy of Sciences (CAS), Beijing (China). Inst. of Theoretical Physics, Key Lab. of Theoretical Physics
  4. Brown Univ., Providence, RI (United States). Dept. of Physics
+ Show Author Affiliations
The relation between the bosonic higher spin W∞[λ]W∞[λ] algebra, the affine Yangian of gl1, and the SHc algebra is established in detail. For generic λ we find explicit expressions for the low-lying W∞[λ] modes in terms of the affine Yangian generators, and deduce from this the precise identification between λ and the parameters of the affine Yangian. Furthermore, for the free field cases corresponding to λ = 0 and λ = 1 we give closed-form expressions for the affine Yangian generators in terms of the free fields. Interestingly, the relation between the W∞ modes and those of the affine Yangian is a non-local one, in general. We also establish the explicit dictionary between the affine Yangian and the SHc generators. Lastly, given that Yangian algebras are the hallmark of integrability, these identifications should pave the way towards uncovering the relation between the integrable and the higher spin symmetries.
Research Organization:
Brown Univ., Providence, RI (United States)
Sponsoring Organization:
Swiss National Science Foundation; USDOE Office of Science (SC)
Grant/Contract Number:
SC0010010
OSTI ID:
1368374
Alternate ID(s):
OSTI ID: 22694218
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 4 Vol. 2017; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (8)

Rectangular W-algebras, extended higher spin gravity and dual coset CFTs journal February 2019
The supersymmetric affine Yangian journal May 2018
Gluing two affine Yangians of 𝔤𝔩1 journal October 2019
Twin-plane-partitions and N $$ \mathcal{N} $$ = 2 affine Yangian journal November 2018
The matrix-extended $$ {\mathcal{W}}_{1+\infty } $$ algebra journal December 2019
The supersymmetric affine Yangian text January 2018
Gluing two affine Yangians of gl(1) text January 2019
Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian text January 2018

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AdS-CFT Correspondence
Conformal and W Symmetry
Higher Spin Symmetry
Quantum Groups