Graviton multi-point amplitudes for higher-derivative gravity in anti-de Sitter space

TL;DR

This paper computes multi-point graviton scattering amplitudes in anti-de Sitter space for higher-derivative gravity theories, providing a general framework for arbitrary derivatives and points, relevant for gauge/gravity duality insights.

Contribution

It introduces a method to derive the general form of n-point amplitudes for higher-derivative gravity in AdS, extending previous calculations to arbitrary derivative orders.

Findings

Derived explicit n-point amplitude formulas for higher-derivative gravity.

Constructed a basis for scattering amplitudes in theories with many derivatives.

Re-expressed scattering properties using Mandelstam variables for specific cases.

Abstract

We calculate graviton multi-point amplitudes in an anti-de Sitter black brane background for higher-derivative gravity of arbitrary order in numbers of derivatives. The calculations are performed using tensor graviton modes in a particular regime of comparatively high energies and large scattering angles. The regime simplifies the calculations but, at the same time, is well suited for translating these results into the language of the dually related gauge theory. After considering theories of up to eight derivatives, we generalize to even higher-derivative theories by constructing a "basis" for the relevant scattering amplitudes. This construction enables one to find the basic form of the n-point amplitude for arbitrary n and any number of derivatives. Additionally, using the four-point amplitudes for six and eight-derivative gravity, we re-express the scattering properties in terms of the Mandelstam variables.