Unraveling conformal gravity amplitudes

TL;DR

This work analyzes tree-level amplitudes in conformal gravity theories, centering on ${\cal N}=4$ conformal supergravity and its minimal/non-minimal variants. It establishes a comprehensive double-copy framework: conformal gravity amplitudes arise from the product of a four-derivative gauge theory $(DF)^2$ with ${\cal N}=4$ SYM, and specific Lagrangians (notably for the Berkovits–Witten theory) reproduce these amplitudes exactly. A key result is the explicit Lagrangian for the non-minimal Berkovits–Witten theory and a precise double-copy prescription for the minimal ${\cal N}=4$ conformal supergravity, including mass-deformed interpolations that connect BW, Weyl, and Einstein supergravities. The study also clarifies state structure in four-derivative theories (planewave vs non-planewave), factorization properties, and how mass deformations help organize amplitudes, with implications for UV behavior and unitarity in conformal gravity. Overall, the paper strengthens the connection between gauge-theory amplitudes and conformal gravity, providing concrete tools for constructing and checking a broad class of amplitudes from dual gauge theories.

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.