Higher Spin Currents in Orthogonal Wolf Space

TL;DR

This paper constructs and explicitly describes higher spin currents in an N=4 superconformal coset theory with an orthogonal Wolf space, extending the understanding of large N=4 holography and operator product expansions.

Contribution

It explicitly derives the WZW affine currents for the N=4 superconformal algebra and constructs higher spin currents, including their OPEs, in the orthogonal Wolf space setting.

Findings

Explicit form of WZW affine currents for N=4 superconformal algebra.

Construction of higher spin currents with detailed OPEs.

Identification of the lowest spin in the multiplet as two, differing from unitary Wolf space.

Abstract

For the N=4 superconformal coset theory by [SO(N+4)/SO(N) x SU(2)] x U(1) (that contains an orthogonal Wolf space) with N=4, the N=2 WZW affine current algebra is obtained. The 16 generators (or 11 generators) of the large N=4 linear (or nonlinear) superconformal algebra are described by these WZW affine currents explicitly. Along the line of large N=4 holography, the extra 16 currents with spins (2,5/2,5/2, 3), (5/2, 3, 3, 7/2), (5/2, 3, 3, 7/2), and (3, 7/2, 7/2, 4) are obtained in terms of the WZW affine currents. The lowest spin of this N=4 multiplet is two rather than one which is for an unitary Wolf space. The operator product expansions (OPEs) between the above 11 currents and these extra 16 higher spin currents are found explicitly.