The operator product expansion between the 16 lowest higher spin currents in the $$\mathcal{N}=4$$ N = 4 superspace

Abstract

Some of the operator product expansions (OPEs) between the lowest 16 higher spin currents of spins (1, (5) SU(3) theory previously. In this paper, by rewriting these OPEs in the N = 4 superspace developed by Schoutens (and other groups), the remaining undetermined OPEs in which the corresponding singular terms possess the composite fields with spins s = 7 2 , 4, 9 2 , 5 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 N = 2 superspace, and using the N = 2 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 N = 2 super OPEs between the four N = 2 higher spin currents denoted by (1,

The next 16 higher spin currents and three-point functions in the large $$\mathcal{N}=4$$ N = 4 holography

“…Using the relations in [6], 12 one can reexpress the currents A ±,i (z) in terms of T μν (z). Furthermore, the higher spin (w) from (3.2) up to an overall factor.…”

“…One of the simplest known OPE in the OPEs between the higher spin 1 current and the other higher spin currents in the context of an extension of the large N = 4 linear superconformal algebra is described by the following OPE [6]:…”

“…The operator product expansions (OPEs) between the lowest 16 higher spin currents of spins (1, [1][2][3][4][5] have been found in [6]. 1 The right hand sides of these OPEs can be written in terms of the above lowest 16 higher spin currents (up to quadratic), the 16 currents which generate the large N = 4 linear superconformal algebra and the next 16 For fixed N with the group G = SU(N + 2) in the N = 4 coset model [4], the explicit results for the lowest (and next) 16 higher spin currents in terms of WZW currents are given 1 The terminology 'large' here (we do not take any limit) is nothing to do with the one in the large N 't Hooft like limit later.…”

“…The next step is to reexpress the right hand sides of the OPEs (written in terms of 16 currents, the lowest 16 higher spin currents and other terms coming from the next 16 higher spin currents in the linear version) in terms of 11 currents and the lowest (and the next) 16 higher spin currents in the nonlinear version with the help of the explicit relations between them [8,12]. Of course, the right hand sides of the OPEs do not contain the above spin 1 current and the four spin 1 2 currents and therefore they have simple form compared to the ones in the linear version [6]. Furthermore, there are also extra terms (the product of the above 11 currents and the lowest 16 higher spin currents which did not appear in the linear version) as well as the terms obtained by simply replacing the terms appearing in the linear version with them in the nonlinear version.…”

Higher spin currents in the enhanced N = 3 $$ \mathcal{N}=3 $$ Kazama-Suzuki model

“…That is, the OPE (F.1) and the above three OPEs (F.4) will appear in the N = 3 version (7.2) in appropriate supersymmetric way as in [59].…”