https://doi.org/10.1140/epjc/s10052-016-4234-2
Regular Article - Theoretical Physics
The operator product expansion between the 16 lowest higher spin currents in the 
superspace
Department of Physics, Kyungpook National University, Taegu, 41566, Korea
* e-mail: ahn@knu.ac.kr
Received:
15
December
2015
Accepted:
25
June
2016
Published online:
11
July
2016
Some of the operator product expansions (OPEs) between the lowest 16 higher spin currents of spins 
in an extension of the large linear superconformal algebra were constructed in superconformal coset 
theory previously. In this paper, by rewriting these OPEs in the superspace developed by Schoutens (and other groups), the remaining undetermined OPEs in which the corresponding singular terms possess the composite fields with spins 
are completely determined. Furthermore, by introducing arbitrary coefficients in front of the composite fields on the right-hand sides of the above complete 136 OPEs, reexpressing them in the 
superspace, and using the OPEs Mathematica package by Krivonos and Thielemans, the complete structures of the above OPEs with fixed coefficient functions are obtained with the help of various Jacobi identities. We then obtain ten 
super OPEs between the four higher spin currents denoted by 
, 
, 
and 
(corresponding 136 OPEs in the component approach) in the superconformal coset 
theory. Finally, we describe them as one single super OPE between the above 16 higher spin currents in the superspace. The fusion rule for this OPE contains the next 16 higher spin currents of spins of 
in addition to the quadratic lowest higher spin multiplet and the large linear superconformal family of the identity operator. The various structure constants (fixed coefficient functions) appearing on the right-hand side of this OPE depend on N and the level k of the bosonic spin-1 affine Kac–Moody current. For convenience, the above 136 OPEs in the component approach for generic (N, k) with simplified notation are given.
© The Author(s), 2016
