All-loop-orders relation between Regge limits of N $$ \mathcal{N} $$ = 4 SYM and N $$ \mathcal{N} $$ = 8 supergravity four-point amplitudes

• Main Author: Stephen G. Naculich
• Format: Article
• Language: English
• Published: SpringerOpen 2021-02-01
• Series: Journal of High Energy Physics
• Subjects: Extended Supersymmetry; Scattering Amplitudes; Supergravity Models; Supersymmetric Gauge Theory
• Online Access: https://doi.org/10.1007/JHEP02(2021)044

Abstract We examine in detail the structure of the Regge limit of the (nonplanar) N $$ \mathcal{N} $$ = 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 ϵ 2 $$ \mathcal{O}\left({\upepsilon}^2\right) $$ at two loops, and through O ϵ 0 $$ \mathcal{O}\left({\upepsilon}^0\right) $$ 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 $$ \mathcal{N} $$ = 8 supergravity four-point amplitude.