Higher Spin Currents in Wolf Space for Generic N

TL;DR

This paper constructs explicit higher spin currents in the N=4 superconformal Wolf space coset, revealing complex tensor structures and their relations within the algebra, advancing understanding of higher spin symmetries in superconformal theories.

Contribution

It provides explicit expressions for 16 higher spin currents with detailed tensor structures in the Wolf space coset for generic N, extending previous algebraic constructions.

Findings

Explicit higher spin currents with detailed tensor structures derived.

Identification of antisymmetric and symmetric tensor contributions in currents.

Enhanced understanding of higher spin symmetries in N=4 superconformal models.

Abstract

We obtain the 16 higher spin currents with spins (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) in the N=4 superconformal Wolf space coset SU(N+2)/[SU(N) x SU(2) x U(1)]. The antisymmetric second rank tensor occurs in the quadratic spin-1/2 Kac-Moody currents of the higher spin-1 current. Each higher spin-3/2 current contains the above antisymmetric second rank tensor and three symmetric (and traceless) second rank tensors (i.e. three antisymmetric almost complex structures contracted by the above antisymmetric tensor) in the product of spin-1/2 and spin-1 Kac-Moody currents respectively. Moreover, the remaining higher spin currents of spins 2, 5/2, 3 contain the combinations of the (symmetric) metric, the three almost complex structures, the antisymmetric tensor or the three symmetric tensors in the multiple product of the above Kac-Moody currents as well as the composite currents from the large N=4 nonlinear superconformal algebra.