Higher-spin charges in Hamiltonian form. I. Bose fields

Abstract

We study asymptotic charges for symmetric massless higher-spin fields on Anti de Sitter backgrounds of arbitrary dimension within the canonical formalism. We first analyse in detail the spin-3 example: we cast Fronsdal's action in Hamiltonian form, we derive the charges and we propose boundary conditions on the canonical variables that secure their finiteness. We then extend the computation of charges and the characterisation of boundary conditions to arbitrary spin.

Asymptotic Charges at Null Infinity in Any Dimension

“…in agreement with the result derived in the Chern-Simons formulation [54,55]. When the dimension of spacetime is equal to three or bigger than four, with our boundary conditions, the spin-three charges thus display a structure very similar to that of the corresponding charges computed on anti de Sitter backgrounds in [59]. The latter, indeed, in the limit of vanishing cosmological constant should reproduce the flat-space charges at spatial infinity.…”

“…so that the two approaches agree in this case. The definition of Q is in principle subject to ambiguities stemming from θ µ → θ µ + ∂ ν λ µν , where λ µν = −λ νµ , which does not alter the variation (59). In the spirit of [40], we may choose to set to zero the corresponding additional terms, precisely because this choice defines an integrable Hamiltonian, as shown above.…”

On higher-spin supertranslations and superrotations

“…Here we employ boundary conditions affine to those usually considered in literature for gravity, implementing the idea that fields should falloff faster at infinity with the increasing of the dimensionality of space-time. 7 In complete analogy, the boundary conditions that give finite higher-spin charges in AdS also satisfy the field equations asymptotically [38,39]. In three space-time dimensions these falloffs have also been proved to remain valid even when interactions are switched on [40].…”

On Exact Solutions and Perturbative Schemes in Higher Spin Theory

“…An alternative framework in which certain 2-and 4-forms in x-space, referred to as the Lagrangian forms, are introduced was proposed in [58], where their possible application for the computation of HS invariant charges and generating functional for the boundary correlations functions were discussed; see also [59] for the computation of such HS charges on black-hole solutions at the first order in the deformation parameters. Asymptotic charges in HS theories have also been described in [60,61,62]. Their relation to the HS charges 12 as well as their evaluation on certain exact solutions will be discussed elsewhere [26].…”