N $$ \mathcal{N} $$ = 2 supersymmetry in the twistor description of higher-spin holography

Abstract

Abstract We study the holographic duality between higher-spin (HS) gravity in 4d and free vector models in 3d, with special attention to the role of N $$ \mathcal{N} $$ = 2 supersymmetry (SUSY). For the type-A bosonic bulk theory, dual to spin-0 fields on the boundary, there exists a twistor-space description; this maps both single-trace boundary operators and linearized bulk fields to spacetime-independent twistor functions, whose HS-algebra products compute all boundary correlators. Here, we extend this description to the type-B bosonic theory (dual to spin-1/2 fields on the boundary), and to the supersymmetric theory containing both. A key role is played by boundary bilocals, which in type-A are dual to the Didenko-Vasiliev 1/2-BPS “black hole”. We extend this to an infinite family of linearized 1/2-BPS “black hole” solutions. Remarkably, the full supersymmetric theory (along with the SUSY generators) fits in the same space of twistor functions as the type-A theory. Instead of two sets of bosonic bulk fields, the formalism sees one set of linearized fields, but with both types of boundary data allowed.

Keywords

• Extended Supersymmetry
• Higher Spin Gravity
• Higher Spin Symmetry
• AdS-CFT Correspondence