Supersymmetric Higher Spin Theories

Understand

We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev.

• We construct the $dS_4$, Euclidean and Kleinian version of these algebras, as well as the corresponding fully nonlinear Vasiliev type higher spin theories, in which the reality conditions we impose on the master fields play a crucial role.
• The ${\cal N}=2$ supersymmetric higher spin theory in $dS_4$, on which we elaborate further, is included in this class of models.
• A subset of Konstein-Vasiliev algebras are the higher spin extensions of the $AdS_4$ superalgebras $osp(4|{\cal N})$ for ${\cal N}=1,2,4$ mod 4 and can be realized using fermionic oscillators.