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

## TL;DR

This paper develops a Hamiltonian formalism to compute asymptotic higher-spin fermionic charges in Anti de Sitter spaces, generalizing supercharge constructions to arbitrary half-integer spins.

## Contribution

It introduces a Hamiltonian approach for higher-spin fermionic charges, extending previous supergravity results to arbitrary spin fields in AdS backgrounds.

## Key findings

- Derived explicit expressions for higher-spin fermionic charges.
- Proposed boundary conditions ensuring charge finiteness.
- Extended the formalism from spin 5/2 to arbitrary half-integer spins.

## 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 half-integer spin. Our construction generalises to higher-spin fermionic gauge fields the known Hamiltonian derivation of supercharges in AdS supergravity.