All-loop-orders relation between Regge limits of N = 4 SYM and N = 8 supergravity four-point amplitudes

A bstract We examine in detail the structure of the Regge limit of the (nonplanar) N N = 4 SYM four-point amplitude. We begin by developing a basis of color factors C ik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through O (²) O ϵ 2 at two loops, and through O (⁰) O ϵ 0 at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the N N = 8 supergravity four-point amplitude.