Higher spin currents with manifest SO(4) symmetry in the large 𝒩 = 4 holography

Abstract

The large [Formula: see text] nonlinear superconformal algebra is generated by six spin-[Formula: see text] currents, four spin-[Formula: see text] currents and one spin-[Formula: see text] current. The simplest extension of these [Formula: see text] currents is described by the [Formula: see text] higher spin currents of spins [Formula: see text]. In this paper, by using the defining operator product expansions (OPEs) between the [Formula: see text] currents and [Formula: see text] higher spin currents, we determine the [Formula: see text] higher spin currents (the higher spin-[Formula: see text] currents were found previously) in terms of affine Kac–Moody spin-[Formula: see text], 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-[Formula: see text] currents. The eigenvalues are computed for coset representations containing at most four boxes, at finite [Formula: see text] and [Formula: see text]. After calculating the eigenvalues of the zeromode of the higher spin-[Formula: see text] current acting on the higher representations up to three (or four) boxes of Young tableaux in [Formula: see text] in the Wolf space coset, we obtain the corresponding three-point functions with two scalar operators at finite [Formula: see text]. Furthermore, under the large [Formula: see text] ’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.