Higher spin currents with manifest S O (4) symmetry in the large = 4 holography

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Abstract

The large = 4 nonlinear superconformal algebra is generated by six spin-1 currents, four spin-3 2 currents and one spin-2 current. The simplest extension of these 11 currents is described by the 16 higher spin currents of spins (1, 3 2, 3 2, 3 2, 3 2, 2, 2, 2, 2, 2, 2, 5 2, 5 2, 5 2, 5 2, 3). In this paper, by using the defining operator product expansions (OPEs) between the 11 currents and 16 higher spin currents, we determine the 16 higher spin currents (the higher spin-1, 3 2 currents were found previously) in terms of affine Kac-Moody spin-1 2, one currents in the Wolf space coset model completely. An antisymmetric second rank tensor, three antisymmetric almost complex structures or the structure constant are contracted with the multiple product of spin-1 2, 1 currents. The eigenvalues are computed for coset representations containing at most four boxes, at finite N and k. After calculating the eigenvalues of the zeromode of the higher spin-3 current acting on the higher representations up to three (or four) boxes of Young tableaux in SU(N + 2) in the Wolf space coset, we obtain the corresponding three-point functions with two scalar operators at finite (N,k). Furthermore, under the large (N,k) 't Hooft-like limit, the eigenvalues associated with any boxes of Young tableaux are obtained and the corresponding three-point functions are written in terms of the 't Hooft coupling constant in simple form in addition to the two-point functions of scalars and the number of boxes.

Original languageEnglish
Article number1850208
JournalInternational Journal of Modern Physics A
Volume33
Issue number35
DOIs
StatePublished - 20 Dec 2018

Keywords

  • AdS/CFT
  • extended conformal symmetry
  • Higher spin symmetry
  • W symmetry

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