Higher Spin Currents in Wolf Space: Part I

Abstract

For the N=4 superconformal coset theory described by SU(N+2)/SU(N) (that contains a Wolf space) with N=3, the N=2 WZW affine current algebra with constraints is obtained. The 16 generators of the large N=4 linear superconformal algebra are described by those WZW affine currents explicitly. By factoring out four spin-1/2 currents and the spin-1 current from these 16 generators, the remaining 11 generators (spin-2 current, four spin-3/2 currents, and six spin-1 currents) corresponding to the large N=4 nonlinear superconformal algebra are obtained. Based on the recent work by Gaberdiel and Gopakumar on the large N=4 holography, the extra 16 currents, with spin contents (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) described in terms of N=2 multiplets, are obtained and realized by the WZW affine currents. As a first step towards N=4 W algebra (which is NOT known so far), the operator product expansions (OPEs) between the above 11 currents and these extra 16 higher spin currents are found explicitly. It turns out that the composite fields with definite U(1) charges, made of above (11+16) currents (which commute with the Wolf space subgroup SU(N=3) x SU(2) x U(1) currents), occur in the right hand sides of these OPEs.

143 pages; Simplified the OPEs using compact notations, manifest SU(2) x SU(2) representations are given and to appear in JHEP

References in corpus (6)

• Large N=4 Holography
• Higher Spin Currents with Arbitrary N in the N=1 Stringy Coset Minimal Model
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• Spin-5 Casimir Operator and Its Three-Point Functions with Two Scalars
• Higher Spin Currents in the Holographic N=1 Coset Minimal Model
• Higher Spin Currents in Wolf Space: Part II

Cited by in corpus (22)

• Higher Spins & Strings
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Higher spin AdS_3 holography with extended supersymmetry
• The symmetry of large N=4 holography
• Extended supersymmetry in AdS_3 higher spin theories
• Rectangular W-(super)algebras and their representations
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• The Operator Product Expansion between the 16 Lowest Higher Spin Currents in the N=4 Superspace
• Higher Spin Currents in Wolf Space: Part II
• Higher Spin Currents in Wolf Space for Generic N
• Higher Spin Currents in Wolf Space: Part III
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• 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
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• Three Point Functions in the N=4 Orthogonal Coset Theory
• Higher Spin Currents in the Orthogonal Coset Theory
• Adding Complex Fermions to the Grassmannian-like Coset Model
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• On the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal holographic dictionary
• Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography