The two-loop five-particle amplitude in N = 8 supergravity

A bstract We compute for the first time the two-loop five-particle amplitude in N = 8 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 penta...

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Published inThe journal of high energy physics Vol. 2019; no. 3; pp. 1 - 23
Main Authors Chicherin, Dmitry, Gehrmann, Thomas, Henn, Johannes M., Wasser, Pascal, Zhang, Yang, Zoia, Simone
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 20.03.2019
Springer Nature B.V
Subjects
Amplitudes
Classical and Quantum Gravitation
Elementary Particles
Gravitons
High energy physics
Permutations
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Supergravity
Symbols
Weight
Supergravity Models
Scattering Amplitudes
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Summary:A bstract We compute for the first time the two-loop five-particle amplitude in N = 8 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. We observe that one of the symbol letters is absent from the amplitude. The latter 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. We extract the finite remainder function, which depends on fewer rational factors. 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 a supplementary file.
ISSN:1029-8479
DOI:10.1007/JHEP03(2019)115