skip to main content


Title: Higher spins and Yangian symmetries

The relation between the bosonic higher spin W∞[λ]W∞[λ] algebra, the affine Yangian of gl 1, and the SH c 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 SH c 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.
 [1] ;  [2] ;  [3] ;  [4]
  1. Federal Inst. of Technology, Zurich (Switzerland). Inst. fur Theoretische Physik
  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
Publication Date:
Grant/Contract Number:
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: 4; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
Brown Univ., Providence, RI (United States)
Sponsoring Org:
USDOE Office of Science (SC); Swiss National Science Foundation (SNSF)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT Correspondence; Conformal and W Symmetry; Higher Spin Symmetry; Quantum Groups
OSTI Identifier: