Supergravity Scattering Amplitudes

TL;DR

This paper compares methods for calculating supergravity scattering amplitudes using Riemann and K"ahler normal coordinates, showing their equivalence at extremal points of the scalar potential in no-scale supergravity models.

Contribution

It introduces a comparison between Riemann and K"ahler normal coordinate methods for supergravity amplitudes and explicitly demonstrates their equivalence at extremal points.

Findings

K"ahler normal coordinates provide a more compact calculation method.

Equivalence of the two methods holds only at extremal points.

Explicit transformations and amplitudes are calculated for specific models.

Abstract

Supergravity theories with non-minimal K\"ahler potentials are characterized by a non-trivial field space manifold with corresponding non-trivial kinetic terms. The scattering amplitudes in these theories can be calculated at fixed background field values by making a field redefinition to Riemann normal coordinates. Because of the K\"ahler structure of supergravity, a more compact method for calculating amplitudes is obtained by a redefinition to K\"ahler normal coordinates. We compare both methods and calculate the explicit transformations and amplitudes for several examples in the context of no-scale supergravity with one and two chiral superfields. We show that in all cases the equivalence of the scattering amplitudes using either Riemann normal or K\"ahler normal coordinates is possible only at extremal points of the scalar potential.