Large N=4 Holography

TL;DR

This work constructs a higher-spin holography framework with large ${\rm N}=4$ supersymmetry by embedding a Vasiliev theory based on ${\rm shs}_2[\mu]$ and a global ${D}(2,1|\alpha)$ subalgebra into a dual two-dimensional coset CFT. The authors identify the bulk symmetry with the wedge of a ${s\tilde{\cal W}}^{(4)}_{\infty}[\gamma]$ algebra and match it to the large ${\rm N}=4$ coset spectrum in the 't Hooft limit, establishing a precise parameter correspondence ${\mu}=\lambda=\gamma$ and linking bulk single-particle states to coset primaries such as $({\rm f};0)$ and $(0;\overline{\rm f})$. They show that the minimal and certain higher representations saturate BPS bounds, and they analyze how a non-linear truncation ${\tilde A}_{\gamma}$ aligns the bulk and boundary algebras, including the role of a decoupled ${\rm u}(1)$ current. Finally, the work discusses a non-abelian generalisation of Vasiliev theory that could describe string theory on ${\rm AdS}_3\times {\rm S}^3\times {\rm S}^3\times {\rm S}^1$, highlighting both the potential and the challenges of embedding these higher-spin constructions into a full string-theoretic setting.

Abstract

The class of 2d minimal model CFTs with higher spin AdS3 duals is extended to theories with large N=4 superconformal symmetry. We construct a higher spin theory based on the global D(2,1|alpha) superalgebra, and propose a large N family of cosets as a dual CFT description. We also indicate how a non-abelian version of this Vasiliev higher spin theory might give an alternative description of IIB string theory on an AdS3 x S3 x S3 x S1 background.