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

Abstract

Sixteen higher spin currents with spins $$ \left(1,\frac{3}{2},\frac{3}{2},2\right) $$ , $$ \left(\frac{3}{2},2,2,\frac{5}{2}\right) $$ , $$ \left(\frac{3}{2},2,2,\frac{5}{2}\right) $$ , and $$ \left(2,\frac{5}{2},\frac{5}{2},3\right) $$ were previously obtained in an extension of the large $$ \mathcal{N}=4 $$ ‘nonlinear’ superconformal algebra in two dimensions. By carefully analyzing the zero-mode eigenvalue equations, three-point functions of bosonic (higher spin) currents are obtained with two scalars for any finite N (where SU(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 $$ \mathcal{N}=4 $$ ‘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.