Double-logarithms in Einstein-Hilbert gravity and supergravity

TL;DR

The authors derive an all-orders resummation of double-logarithmic in-energy corrections to four-graviton scattering in Einstein-Hilbert gravity and various supergravities. Using an infrared evolution equation that accounts for ladder and non-ladder diagrams, they obtain a Mellin-space representation with a resummed function Φ^{(N)}(ξ), where ξ = α|t| ln^2(s/|q|^2), and analyze the high-energy behavior across different N. They show that amplitudes grow for N<4, are critical at N=4, and decay for N>4, with explicit even-N solutions via a Schrödinger-type mapping and special cases (e.g., N=8) expressed through erfc-like integrals; the N=4 case yields pure Regge behavior. The two-loop truncation matches known results for N=4–8 and EH gravity, providing a strong cross-check and informing the UV properties of supergravity theories.

Abstract

We study the interplay between graviton reggeization and double-logarithmic in energy contributions to four-graviton scattering in theories with and without supersymmetry. Predictions to all orders in the gravitational coupling are given for these double-logarithms. As the number of supersymmetries grows these terms generate a convergent behaviour for the amplitudes at very high energies. At two-loop level, we find agreement with previous exact results for N=8 supergravity and with those of Boucher-Veronneau and Dixon, who studied the N=4,5,6 supergravities using a conjectured double-copy structure of gravity.

Figures (4)

• Figure 1: Scattering amplitude for $N=0,1,2,3,4,5, 6,7,8$.
• Figure 2: Scattering amplitude for $N=0,1,2,3$.
• Figure 3: Scattering amplitude for $N=5,6$.
• Figure 4: Scattering amplitude for $N=7,8$.