Abstract
Recently, a 2d coset model with $$ \mathcal{N}=3 $$ superconformal symmetry was pro-posed to be holographic dual to a higher spin supergravity on AdS3 and the relation to superstring theory was discussed. However, away from the tensionless limit, there is no higher spin symmetry and the higher spin states are massive. In this paper, we examine the deformations of the coset model which preserve $$ \mathcal{N}=3 $$ superconformal symmetry, but break generic higher spin symmetry. We focus on double-trace type deformations which are dual to changes of boundary conditions for the bulk matter fields. In the bulk theory, the symmetry breaking will generate mass for the higher spin fields. As a concrete example, we compute the Higgs mass of a spin 2 field both from the bulk and the boundary theory.
Highlights
These no-go theorems do not apply for a theory with a curved background, and Vasiliev theory constitutes a famous example of a non-trivial higher spin gauge theory defined on AdS space [3]
We examine the deformations of the coset model which preserve N = 3 superconformal symmetry, but break generic higher spin symmetry
In order to construct the model with extended supersymmetry, we utilize the fact that the factor su(N + M )N+M can be described by free fermions ΨA in the adjoint representation of su(N + M )
Summary
In [11] a higher spin AdS/CFT duality was proposed involving the N = 2 supersymmetric version of Prokushkin-Vasiliev theory with M ′ × M ′ matrix valued fields introduced in [17]. The higher spin theory includes a parameter λ, which determines the gauge algebra denoted by shsM′[λ] as well as the mass of the matter fields. The Kazama-Suzuki coset in (1.2) is dual to the higher spin theory, but with a U(M ). For the theory dual to the Kazama-Suzuki model (1.2) we assign the U(M ) invariant condition. Even under this condition, the shsT2 [1/2] subalgebra survives and the theory still has N = 3 supersymmetry. For the theory dual to (1.2) we further need to assign the U(M ) invariant condition
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