Higher Spin Currents in Wolf Space: Part II

TL;DR

This paper extends the known higher spin currents in an N=4 superconformal Wolf space coset model by calculating operator product expansions, revealing new currents and their algebraic structure within the extended superconformal algebra.

Contribution

It computes the next set of higher spin currents and their OPEs in the N=4 superconformal Wolf space coset, expanding the algebraic understanding of these models.

Findings

Determined 16 new higher spin currents from OPE calculations.

Identified quadratic and linear composite fields in the OPEs.

Revealed fusion rules involving large N=4 superconformal currents.

Abstract

The 16 lowest higher spin currents of 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 terms of N=2 WZW affine currents were obtained in the N=4 superconformal Wolf space coset SU(5)/[SU(3) x SU(2) x U(1)] previously. By calculating the operator product expansions (OPEs) between the above higher spin currents which are contained in an extension of large N=4 nonlinear superconformal algebra, the next 16 higher spin currents of 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 determined from the right hand sides of these OPEs. Moreover, the composite fields consisting of both the 11 currents in the large N=4 nonlinear superconformal algebra and the above 16 lowest higher spin currents also occur in the right hand sides of these OPEs. The latter appears quadratically (and linearly) in the fusion rules together with large N=4 nonlinear superconformal family of the identity operator.