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The two-loop five-particle amplitude in \( \mathcal{N} \) = 8 supergravity

Journal of High Energy Physics volume 2019, Article number: 115 (2019) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We compute for the first time the two-loop five-particle amplitude in \( \mathcal{N} \) = 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.

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Authors and Affiliations

  1. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805, München, Germany

    Dmitry Chicherin, Johannes M. Henn, Yang Zhang & Simone Zoia

  2. Physik-Institut, Universität Zürich, Wintherturerstrasse 190, CH-8057, Zürich, Switzerland

    Thomas Gehrmann

  3. PRISMA Cluster of Excellence, Johannes Gutenberg University, D-55128, Mainz, Germany

    Pascal Wasser

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  1. Dmitry Chicherin
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  2. Thomas Gehrmann
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  3. Johannes M. Henn
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  4. Pascal Wasser
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  5. Yang Zhang
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Correspondence to Dmitry Chicherin.

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ArXiv ePrint: 1901.05932

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Chicherin, D., Gehrmann, T., Henn, J.M. et al. The two-loop five-particle amplitude in \( \mathcal{N} \) = 8 supergravity. J. High Energ. Phys. 2019, 115 (2019). https://doi.org/10.1007/JHEP03(2019)115

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Keywords

  • Scattering Amplitudes
  • Supergravity Models