On higher spin symmetries in AdS 5

Abstract

A special embedding of the SU(4) algebra in SU(10), including both spin two and spin three symmetry generators, is constructed. A possible five dimensional action for massless spin two and three fields with cubic interaction is constructed. The connection with the previously investigated higher spin theories in AdS 5 background is discussed. Generalization to the more general case of symmetries, including spins 2, 3, . . . s, is shown. * These algebras should correspond to the representations of su(2, 2) (the latter can serve as defining representations for these algebras) found in [14] and should be discrete cases of the one-parameter family of algebras of [15]. * The identity (A.16) relates two possible expressions for the spin 2 action.

Notes on higher-spin algebras: minimal representations and structure constants

“…As we have seen in the 3D case, the presence of the asymptotic boundary may provoke a deformation of global symmetry invalidating this condition. This phenomenon is in principle possible in any odd D dimensions, so may provide a chance for a consistent HS theory with a finite field content -see [65] for a recent attempt.…”

“…Such finite-dimensional HS algebras have been considered recently in [65] -see section 4.1 for more details.…”

“…Finally, the trilinear form is given by 65) and the integral can be evaluated, by expanding the denominator, as…”

“…, a M ) can take. For the N = 4 case of sl 4 ≃ so 6 , the 5D finite-dimensional HS algebras have been obtained in [65] making use of the decomposition of sl ( M +3 M ) generators into traceless tensors of sl 4 .…”

New conformal higher spin gravities in 3d

“…explicit structure constants [20,58]. It was also found in various contexts [19,20,59] that there are certain finite dimensional algebras that can be viewed as higher spin algebras, at least up to some point. 2 Below we extend this class of finite dimensional algebras.…”