Three point functions in the large N = 4 $$ \mathcal{N}=4 $$ holography

Abstract

Sixteen higher spin currents with spins (1, N + 2) is the group of coset) and k (the level of spin-1 Kac Moody current). Furthermore, these 16 higher spin currents are implicitly obtained in an extension of large N = 4 'linear' superconformal algebra for generic N and k. The corresponding three-point functions are also determined. Under the large N 't Hooft limit, the two corresponding three-point functions in the nonlinear and linear versions coincide even though they are completely different for finite N and k.

The next 16 higher spin currents and three-point functions in the large $$\mathcal{N}=4$$ N = 4 holography

“…One can describe the remaining half of the SU(N + 2) indices in (2.2) with * similarly. See the reference [22] for the nontrivial diagonal generators with complex elements.…”

“…The three almost complex structures (h 1 , h 2 , h 3 ) appearing in (2.1) are given by the following 4N × 4N matrices (in the notation of [22]): analyze the h 2 and h 3 matrices according to the coset indices (2.3). 6 2.2 The large N = 4 nonlinear superconformal algebra…”

“…Of course, the 11 currents in (2.1) or (4.1) are regular in the OPEs between them and the spin .2) as follows [22]:…”

“…Moreover, they are 2 representation under the SU(2). One further introduces the following states [22]:…”

“…4 See also the relevant work in [19][20][21]. The three-point functions of the (bosonic) higher spin 1, 2, 3 currents (which are member of the above lowest 16 higher spin currents) both in the linear and nonlinear versions with two scalars have been found in [22]. One of the main features of this construction is that we do not have to obtain the explicit results for the higher spin currents in terms of WZW affine KacMoody currents for generic N (and k) manually where the bosonic spin 1 affine Kac-Moody current has the level k, contrary to the other cases where the complete results are needed [23][24][25][26][27][28][29][30] in the context of [31][32][33] except for the overall factor.…”