Graviton scattering amplitudes and Pure Connection Formulation of GR

TL;DR

This paper demonstrates that the Pure Connection Formulation simplifies the computation of graviton scattering amplitudes, extends to broader gravitational theories, and reveals new parity-violating amplitudes beyond General Relativity.

Contribution

It introduces a simplified formalism for graviton scattering calculations that generalizes to wider gravitational theories and uncovers novel parity-violating amplitudes.

Findings

Simplified Feynman rules in the Pure Connection Formulation

Computed all tree-level graviton scattering amplitudes for a broad class of theories

Discovered new parity-violating amplitudes in non-GR theories

Abstract

We show how the recently introduced "Pure Connection Formulation" of gravity provides a natural framework for approaching the problem of computing graviton scattering amplitudes. In particular, we show that the interaction vertices are greatly simplified in this formalism as compared to the Einstein-Hilbert perturbation theory. This, in turns, leads to very simple Feynman rules that we employ for the direct computations. Furthermore, this framework naturally extends to wider class of gravitational theories, which encompasses General Relativity as a special case. We compute all the possible tree-level graviton-graviton scattering amplitudes for a general theory from this class. In the GR case the results are in complete accordance with the known expressions in the literature. Moreover, for the general theory distinct from GR, we find new tree-level parity-violating amplitudes. The presence of this new amplitudes is a direct consequence of the fact that the general theory does not exhibit explicit parity invariance.