The large $\mathcal{N}=4$ superconformal ${\mathcal{W}}_{\infty }$ algebra

Abstract

The most general large $\mathcal{N}=4$ superconformal ${\mathcal{W}}_{\infty }$ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the ${\mathcal{W}}_{\infty }$ algebra is uniquely determined by the levels of the two $\mathfrak{su}(2)$ algebras, a conclusion that holds both for the linear and the non-linear case. We also perform various cross-checks of our analysis, and exhibit two different types of truncations in some detail.

37 pages; v2: reference added and typo fixed

References in corpus (3)

• The Holographic Dual of AdS3 x S3 x S3 x S1
• The symmetry of large N=4 holography
• On the coset duals of extended higher spin theories

Cited by in corpus (13)

• Higher Spins & Strings
• Higher spin AdS_3 holography with extended supersymmetry
• The symmetry of large N=4 holography
• Extended supersymmetry in AdS_3 higher spin theories
• Higher spins in the symmetric orbifold of K3
• The Continuous Orbifold of N=2 Minimal Model Holography
• Higgs phenomenon for higher spin fields on AdS_3
• 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
• Marginal deformations and the Higgs phenomenon in higher spin AdS_3 holography
• Adding Complex Fermions to the Grassmannian-like Coset Model
• The $\mathfrak{so}$-Kazama-Suzuki Models at Large Level
• The Small $\mathcal{N}=4$ Superconformal ${\mathcal{W}}_{\infty }$ Algebra