The Central Emission Vertex of two gravitons

It has recently been shown that there exists an $s$-channel sequence of classical corrections to the $H$ diagram computed long ago by Amati, Ciafaloni and Veneziano. At leading logarithmic accuracy, those corrections feature the gravity BFKL kernel as a crucial element, and may be computed through either rapidity renormalisation group equations or amplitudes built through $s$-channel unitarity cuts. In this paper, we evaluate six-graviton amplitudes in next-to-multi-Regge kinematics, and compute for the first time the Central Emission Vertex for the emission of two gravitons, which is relevant to evaluate the corrections to the gravity BFKL kernel, and thus to go beyond the leading logarithmic accuracy.