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See detailHigher Spin Gravity Amplitudes From Zero-form Charges
Colombo, Nicolo UL; Sundell, Per

E-print/Working paper (2012)

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 ... [more ▼]

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 [less ▲]

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See detailA minimal BV action for Vasiliev's four-dimensional higher spin gravity
Boulanger, Nicolas; Colombo, Nicolo UL; Sundell, Per

in Journal of High Energy Physics [=JHEP] (2012)

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to ... [more ▼]

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle. [less ▲]

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See detailTwistor space observables and quasi-amplitudes in 4D higher spin gravity
Colombo, Nicolo UL; Sundell, Per

in Journal of High Energy Physics [=JHEP] (2010)

Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this ... [more ▼]

Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this induces a map from a generally covariant formulation in spacetime with higher-derivative interactions to a formulation in terms of a deformed symplectic structure on a noncommutative doubled twistor space, sending spacetime boundary conditions to various sectors of an associative star-product algebra. We look at observables given by integrals over twistor space defining composite zero-forms in spacetime that do not break any local symmetries and that are closed on shell. They can be evaluated locally in spacetime and interpreted as building blocks for dual amplitudes. To regularize potential twistor-space divergencies arising in their curvature expansion, we propose a closed-contour prescription that respects associativity and hence higher-spin gauge symmetry. As a sample calculation, we examine next-to-leading corrections to quasi-amplitudes for twistor-space plane waves, and find cancellations that we interpret using transgression properties in twistor space. [less ▲]

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