Supersymmetric Higher Spin Theories

Abstract

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 $d{S}_4$, 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 $\mathcal{N}=2$ supersymmetric higher spin theory in $d{S}_4$, 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 $Ad{S}_4$ superalgebras $osp(4|\mathcal{N})$ for $\mathcal{N}=1,2,4$ mod 4 and can be realized using fermionic oscillators. We tensor the higher superalgebras of the latter kind with appropriate internal symmetry groups and show that the $\mathcal{N}=3$ mod 4 higher spin algebras are isomorphic to those with $\mathcal{N}=4$ mod 4. We describe the fully nonlinear higher spin theories based on these algebras as well, and we elaborate further on the $\mathcal{N}=6$ supersymmetric theory, providing two equivalent descriptions one of which exhibits manifestly its relation to the $\mathcal{N}=8$ supersymmetric higher spin theory.

30 pages. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev

References in corpus (3)

• Chern-Simons Theory with Vector Fermion Matter
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Real Forms of Complex Higher Spin Field Equations and New Exact Solutions

Cited by in corpus (25)

• What if string theory has no de Sitter vacua?
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Mixed-symmetry fields in de Sitter space: a group theoretical glance
• Unconstrained off-shell superfield formulation of $4D,\mathcal{N}=2$ supersymmetric higher spins
• Uniformizing higher-spin equations
• Cubic Vertices for N=1 Supersymmetric Massless Higher Spin Fields in Various Dimensions
• Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?
• Minimal model of Chiral Higher Spin Gravity
• A Compendium of Sphere Path Integrals
• Chiral Higher Spin Gravity and Convex Geometry
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• Higher Spins in Hyper-Superspace
• Supersymmetric dS/CFT
• An Action for Matter Coupled Higher Spin Gravity in Three Dimensions
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• Frobenius-Chern-Simons gauge theory
• Action principles for higher and fractional spin gravities
• Higher spin fluctuations on spinless 4D BTZ black hole
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• Frame- and Metric-like Higher-Spin Fermions
• Constructing the bulk at the critical point of three-dimensional large $N$ vector theories
• Instantons in AdS${}_4$ From (anti)Membranes Wrapping $S^7$ To Bose-Fermi Duality in CFT${}_3$'s
• Representations of the Lie Superalgebra $\mathfrak{osp}(1|2n)$ with Polynomial Bases
• Diagonalization Procedure for Reducible Massless N=1 Supermultiplets