Yangian of AdS3/CFT2 and its deformation

2015/03/31 by Vidas Regelskis
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Duality (order theory) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #String (physics) #Superalgebra #Worldsheet #Yangian #hep-th #math-ph #math.MP #math.QA #msc:81Q80 #msc:81R10 #msc:81R12 #msc:81T30

paper · pdf · doi:10.1016/j.geomphys.2016.04.001

21 pages, 1 figure. Final version. Accepted to J. Geom. and Phys

openalex publication_date 2016/04/11 · arxiv created 2016/04/21 · arxiv updated 2016/04/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

We construct highest-weight modules and a Yangian extension of the centrally extended sl(1|1)² superalgebra, that is a symmetry of the worldsheet scattering associated with the AdS3/CFT3 duality. We demonstrate that the R-matrix intertwining atypical modules is of a trigonometric type. We also consider a quantum deformation of this superalgebra, its modules, and obtain a quantum affine extension of the Drinfeld-Jimbo type that describes a deformed worldsheet scattering.

Citations

• The AdS₃× S³× S³\timesS¹ worldsheet S matrix
• Generalised integrable Hubbard models
• The nested Bethe ansatz for ‘all’ closed spin chains
• Secret symmetries of type IIB superstring theory on \rm Ad\rm S₃ × S³ × M⁴
• The gl (M|N) super Yangian and its finite-dimensional representations
• Hopf algebra structure of the AdS/CFTS-matrix
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• The magnon kinematics of the AdS/CFT correspondence
• Representations of centrally extended Lie superalgebra \mathfrak psl(2|2)psl(2|2)
• Quantization of Lie Groups and Lie Algebras