The = 4 coset model and the higher spin algebra

Changhyun Ahn, Dong Gyu Kim, Man Hea Kim

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9 Scopus citations

Abstract

By computing the operator product expansions between the first two = 4 higher spin multiplets in the unitary coset model, the (anti-)commutators of higher spin currents are obtained under the large (N,k) 't Hooft-like limit. The free field realization with complex bosons and fermions is presented. The (anti-)commutators for generic spins s1 and s2 with manifest SO(4) symmetry at vanishing 't Hooft-like coupling constant are completely determined. The structure constants can be written in terms of the ones in the = 2 ∞ algebra found by Bergshoeff, Pope, Romans, Sezgin and Shen previously, in addition to the spin-dependent fractional coefficients and two SO(4) invariant tensors. We also describe the = 4 higher spin generators, by using the above coset construction results, for general superspin s in terms of oscillators in the matrix generalization of AdS3 Vasiliev higher spin theory at nonzero 't Hooft-like coupling constant. We obtain the = 4 higher spin algebra for low spins and present how to determine the structure constants, which depend on the higher spin algebra parameter, in general, for fixed spins s1 and s2.

Original languageEnglish
Article number2050046
JournalInternational Journal of Modern Physics A
Volume35
Issue number11-12
DOIs
StatePublished - 30 Apr 2020

Keywords

  • AdS/CFT
  • coset model
  • higher spin theory
  • W symmetry

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