Higher Spin Gravity Amplitudes From Zero-form Charges

TL;DR

This paper explores zero-form charges in Vasiliev's higher spin gravity, showing they can generate boundary correlation functions and proposing a new expression for the free energy based on these charges.

Contribution

It introduces a method to compute higher spin amplitudes from zero-form charges and connects them to boundary correlators in conformal field theories.

Findings

Computed two- and three-point functions matching free scalar and fermion theories.

Established a link between zero-form charges and boundary correlation functions.

Proposed a new expression for free energy in higher spin gravity.

Abstract

We examine zero-form charges in Vasiliev's four-dimensional bosonic higher spin gravities. These are classical observables given by integrals over noncommutative twistor space of adjoint combinations of the zero-form master fields, including insertions of delta functions in the deformed oscillators serving as gauge invariant regulators. The regularized charges admit perturbative expansions in terms of multi-linear functionals in the Weyl zero-form, which are Bose symmetric and higher spin invariant by construction, and that can be interpreted as basic building blocks for higher spin gravity amplitudes. We compute two- and three-point functions by attaching external legs given by unfolded bulk-to-boundary propagators, and identify the result with the two- and three-current correlation functions in theories of free conformal scalars and fermions in three dimensions. Modulo assumptions on the structure of the sub-leading corrections, and relying on the generalized Hamiltonian off-shell formulation, we are thus led to propose an expression for the free energy as a sum of suitably normalized zero-form charges