On Classical Solutions of 4d Supersymmetric Higher Spin Theory

Abstract

We present a simple construction of solutions to the supersymmetric higher spin theory based on solutions to bosonic theories. We illustrate this for the case of the Didenko-Vasiliev solution in arXiv:0906.3898, for which we have found a striking simplification where the higher-spin connection takes the vacuum value. Studying these solutions further, we check under which conditions they preserve some supersymmetry in the bulk, and when they are compatible with the boundary conditions conjectured to be dual to certain 3d SUSY Chern-Simons-matter theories. We perform the analysis for a variety of theories with $\mathcal{N}$ = 2, $\mathcal{N}$ = 3, $\mathcal{N}$ = 4 and $\mathcal{N}$ = 6 and find a rich spectrum of $1/4$, $1/3$ and $1/2$-BPS solutions.

v2: 42 pages, section 5 extended, reference added. Version to appear in JHEP

References in corpus (4)

• Fractional M2-branes
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Real Forms of Complex Higher Spin Field Equations and New Exact Solutions
• An axial gauge ansatz for higher spin theories

Cited by in corpus (5)

• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• Planar solutions of higher-spin theory. Nonlinear corrections
• Planar solutions of higher-spin theory I: free field level
• Star-Product Functions in Higher-Spin Theory and Locality
• Higher-spin initial data in twistor space with complex stargenvalues