Higher-spin charges in Hamiltonian form. II. Fermi fields

Abstract

Abstract:We build the asymptotic higher-spin charges associated with "improper" gauge transformations for fermionic higher-spin gauge fields on Anti de Sitter backgrounds of arbitrary dimension. This is achieved within the canonical formalism. We consider massless fields of spin s+1/2, described by a symmetric spinor-tensor of rank s in the Fang-Fronsdal approach. We begin from a detailed analysis of the spin 5/2 example, for which we cast the Fang-Fronsdal 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 halfinteger spin. Our construction generalises to higher-spin fermionic gauge fields the known Hamiltonian derivation of supercharges in AdS supergravity.

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].…”

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

“…Similarly, higher-spin Lie algebras emerge when considering commutators of gauge transformations induced by cubic vertices and restricted to gauge parameters that at linearised level leave the AdS background invariant [65,66]. It will be interesting to compare this analysis with that of surface charges developed in this and the related papers [14,27]. Note that the analysis of asymptotic symmetries in [9,40] also involves ingredients that go beyond the linearised regime, like the full knowledge of the higher-spin gauge algebra on which the bulk theory is built upon.…”

“…A companion paper is devoted to symmetric massless fermionic fields [27]. On the one hand, our work fits within a wider program of improving the grasp over the Hamiltonian description of bosonic higher-spin theories [28][29][30].…”

Frame- and Metric-Like Higher-Spin Fermions

“…The metric-like description of higher-spin gauge fermions in flat-space is easily obtained by taking the limit l → ∞ of the gauge invariant system (A7)-(A12). The degrees of freedom count in flat [13] and AdS [14] spaces are of course the same and given by:…”

“…Originally developed by Fronsdal [9,10] and Fang-Fronsdal [11,12], it encodes the degrees of freedom of higher-spin particles in symmetric tensors and tensor-spinors. In this approach, the construction of a gauge-invariant action for a higher-spin field requires that the field and the gauge parameter obey some off-shell algebraic constraints (see [13,14] for a recent review). Note that the latter requirement can be avoided by recourse to other formulations [15][16][17][18][19][20][21][22][23][24] (see Appendix A).…”