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A tale of two exponentiations in N = 8 supergravity at subleading level

Date: 2020-03-01

Creator: Paolo Di Vecchia, Stephen G. Naculich, Rodolfo Russo, Gabriele Veneziano, Chris D., White

Access: Open access

High-energy massless gravitational scattering in N = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in ϵ, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

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

Date: 2021-02-01

Creator: Stephen G. Naculich

Access: Open access

We examine in detail the structure of the Regge limit of the (nonplanar) N = 4 SYM four-point amplitude. We begin by developing a basis of color factors Cik 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) at two loops, and through O(ϵ) 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 = 8 supergravity four-point amplitude.