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The Number Theory of Superstring Amplitudes

  • Oliver SchlottererEmail author
Conference paper
  • 37 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 314)

Abstract

The following article is intended as a survey of recent results at the interface of number theory and superstring theory. We review the expansion of scattering amplitudes—central observables in field and string theory—in the inverse string tension where elegant patterns of multiple zeta values occur. More specifically, the Drinfeld associator and the Hopf algebra structure of motivic multiple zeta values are shown to govern tree-level amplitudes of the open superstring. Partial results on the quantum corrections are discussed where elliptic analogues of multiple zeta values play a central r\(\hat{\text {o}}\)le.

Keywords

Scattering amplitudes Superstring theory Multiple zeta values Hopf algebras 

Notes

Acknowledgements

I am very grateful to Johannes Broedel, Carlos Mafra, Nils Matthes, Stephan Stieberger and Tomohide Terasoma for collaboration on the projects on which this article is based. Moreover, I would like to thank Johannes Broedel, Nils Matthes and Federico Zerbini for valuable comments on the draft. I am indebted to the organizers of the conference “Numbers and Physics” in Madrid in September 2014 which strongly shaped the research directions leading to [16, 53] and possibly further results. I also acknowledge financial support by the European Research Council Advanced Grant No. 247252 of Michael Green.

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Authors and Affiliations

  1. 1.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutPotsdamGermany
  2. 2.Department of Physics and AstronomyUppsala UniversityUppsalaSweden

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