Higher Spin Currents in Wolf Space: Part I

Understand

For the N=4 superconformal coset theory described by SU(N+2)/SU(N) (that contains a Wolf space) with N=3, the N=2 WZW affine current algebra with constraints is obtained.

• The 16 generators of the large N=4 linear superconformal algebra are described by those WZW affine currents explicitly.
• By factoring out four spin-1/2 currents and the spin-1 current from these 16 generators, the remaining 11 generators (spin-2 current, four spin-3/2 currents, and six spin-1 currents) corresponding to the large N=4 nonlinear superconformal algebra are obtained.
• Based on the recent work by Gaberdiel and Gopakumar on the large N=4 holography, the extra 16 currents, with spin contents (1, 3/2, 3/2, 2), (3/2, 2, 2, 5/2), (3/2, 2, 2, 5/2), and (2, 5/2, 5/2, 3) described in terms of N=2 multiplets, are obtained and realized by the WZW affine currents.