On Classical Solutions of 4d Supersymmetric Higher Spin Theory

TL;DR

This paper constructs simple solutions to 4d supersymmetric higher spin theories, exploring their supersymmetry preservation and boundary conditions, revealing a variety of BPS solutions across different supersymmetry levels.

Contribution

It introduces a straightforward method to generate solutions from bosonic theories and analyzes their supersymmetry properties in various 3d dual boundary theories.

Findings

Found solutions with various BPS fractions (1/4, 1/3, 1/2)

Simplified the higher-spin connection in specific solutions

Analyzed compatibility with boundary conditions for multiple supersymmetries

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.