Unraveling conformal gravity amplitudes

TL;DR

This paper explores the calculation of conformal supergravity amplitudes using double-copy methods, compares them with direct Lagrangian-based calculations, and uncovers new Lagrangians and prescriptions for various theories.

Contribution

It derives a Lagrangian for non-minimal Berkovits-Witten conformal supergravity and establishes the double-copy prescription for minimal ${ m N}=4$ conformal supergravity.

Findings

Derived a Lagrangian for non-minimal Berkovits-Witten theory.

Uncovered the double-copy prescription for minimal ${ m N}=4$ conformal supergravity.

Compared double-copy results with direct Lagrangian calculations.

Abstract

Conformal supergravity amplitudes are obtained from the double-copy construction using gauge-theory amplitudes, and compared to direct calculations starting from conformal supergravity Lagrangians. We consider several different theories: minimal ${\cal N}=4$ conformal supergravity, non-minimal ${\cal N}=4$ Berkovits-Witten conformal supergravity, mass-deformed versions of these theories, as well as supersymmetry truncations thereof. Coupling the theories to a Yang-Mills sector is also considered. For all cases we give the gravity Lagrangians that the double copy implicitly generates. The two main results are: we determine a Lagrangian for the non-minimal Berkovits-Witten theory, and we uncover the double-copy prescription for the minimal ${\cal N}=4$ conformal supergravity.