The Operator Product Expansion between the 16 Lowest Higher Spin Currents in the N=4 Superspace

Abstract

Some of the operator product expansions (OPEs) between the lowest 16 higher spin currents of spins (1, 3/2, 3/2, 3/2, 3/2, 2, 2, 2, 2, 2, 2, 5/2, 5/2, 5/2, 5/2, 3) in an extension of the large N=4 linear superconformal algebra were constructed in the N=4 superconformal coset SU(5)/SU(3) theory previously. In this paper, by rewriting the above OPEs in the N=4 superspace developed by Schoutens (and other groups), the remaining undetermined OPEs where the corresponding singular terms possess the composite fields with spins s =7/2, 4, 9/2, 5 are completely determined. Furthermore, by introducing the arbitrary coefficients in front of the composite fields in 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. Then one obtains ten N=2 super OPEs between the four N=2 higher spin currents denoted by (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) (corresponding 136 OPEs in the component approach) in the N=4 superconformal coset SU(N+2)/SU(N) theory. Finally, one describes them as one single N=4 super OPE between the above sixteen higher spin currents in the N=4 superspace. The fusion rule for this OPE contains the next 16 higher spin currents of spins of (2, 5/2, 5/2, 5/2, 5/2, 3, 3, 3, 3, 3, 3, 7/2, 7/2, 7/2, 7/2, 4) in addition to the quadratic N=4 lowest higher spin multiplet and the large N=4 linear superconformal family of the identity operator. The various structure constants (fixed coefficient functions) appearing in the right hand side of this OPE depend on N and the level k of the bosonic spin-1 affine Kac-Moody current.

412 pages

References in corpus (9)

• Higher Spins & Strings
• Higher spin AdS_3 holography with extended supersymmetry
• Higher spins in the symmetric orbifold of K3
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• Higher Spin Currents in Wolf Space: Part II
• Higher Spin Currents in Orthogonal Wolf Space
• Higher Spin Currents in Wolf Space: Part III
• Higgs phenomenon for higher spin fields on AdS_3
• Three Point Functions in the Large N=4 Holography

Cited by in corpus (14)

• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• The Next $16$ Higher Spin Currents and Three-Point Functions in the Large $\mathcal{N}=4$ Holography
• Three Point Functions in the N=4 Orthogonal Coset Theory
• Higher Spin Currents in the Orthogonal Coset Theory
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• Adding Complex Fermions to the Grassmannian-like Coset Model
• The Grassmannian-like Coset Model and the Higher Spin Currents
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography
• Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography
• Fermionic Construction in the Supersymmetric Coset Model
• The Small $\mathcal{N}=4$ Superconformal ${\mathcal{W}}_{\infty }$ Algebra