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 lowlying 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 closedform 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 nonlocal 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.
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[4]}
 Federal Inst. of Technology, Zurich (Switzerland). Inst. fur Theoretische Physik
 International Centre for Theoretical SciencesTIFR, Bengaluru (India)
 Chinese Academy of Sciences (CAS), Beijing (China). Inst. of Theoretical Physics, Key Lab. of Theoretical Physics
 Brown Univ., Providence, RI (United States). Dept. of Physics
 Publication Date:
 Grant/Contract Number:
 SC0010010
 Type:
 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 10298479
 Publisher:
 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
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdSCFT Correspondence; Conformal and W Symmetry; Higher Spin Symmetry; Quantum Groups
 OSTI Identifier:
 1368374
Gaberdiel, Matthias R., Gopakumar, Rajesh, Li, Wei, and Peng, Cheng. Higher spins and Yangian symmetries. United States: N. p.,
Web. doi:10.1007/JHEP04(2017)152.
Gaberdiel, Matthias R., Gopakumar, Rajesh, Li, Wei, & Peng, Cheng. Higher spins and Yangian symmetries. United States. doi:10.1007/JHEP04(2017)152.
Gaberdiel, Matthias R., Gopakumar, Rajesh, Li, Wei, and Peng, Cheng. 2017.
"Higher spins and Yangian symmetries". United States.
doi:10.1007/JHEP04(2017)152. https://www.osti.gov/servlets/purl/1368374.
@article{osti_1368374,
title = {Higher spins and Yangian symmetries},
author = {Gaberdiel, Matthias R. and Gopakumar, Rajesh and Li, Wei and Peng, Cheng},
abstractNote = {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 lowlying 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 closedform 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 nonlocal 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.},
doi = {10.1007/JHEP04(2017)152},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2017,
place = {United States},
year = {2017},
month = {4}
}