The two-loop five-particle amplitude in supergravity
arXiv:1901.05932 · doi:10.1007/JHEP03(2019)115
Abstract
We compute for the first time the two-loop five-particle amplitude in supergravity. Starting from the known integrand, we perform an integration-by-parts reduction and express the answer in terms of uniform weight master integrals. The latter are known to evaluate to non-planar pentagon functions, described by a 31-letter symbol alphabet. We express the final result for the amplitude in terms of uniform weight four symbols, multiplied by a small set of rational factors. The amplitude satisfies the expected factorization properties when one external graviton becomes soft, and when two external gravitons become collinear. We verify that the soft divergences of the amplitude exponentiate, and extract the finite remainder function. The latter depends on fewer rational factors, and is independent of one of the symbol letters. By analyzing identities involving rational factors and symbols we find a remarkably compact representation in terms of a single seed function, summed over all permutations of external particles. Finally, we work out the multi-Regge limit, and present explicitly the leading logarithmic terms in the limit. The full symbol of the IR-subtracted hard function is provided as an ancillary file.
22 pages, 1 figure, 8 ancillary files
References in corpus (7)
- Classical Polylogarithms for Amplitudes and Wilson Loops
- Algorithm FIRE -- Feynman Integral REduction
- Scattering amplitudes over finite fields and multivariate functional reconstruction
- Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
- On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
- Two-loop graviton scattering relation and IR behavior in N=8 supergravity
- Four-point Amplitudes in N=8 Supergravity and Wilson Loops