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Modular and Holomorphic Graph Functions from Superstring Amplitudes

  • Federico ZerbiniEmail author
Chapter
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)

Abstract

We compare two classes of functions arising from genus-one superstring amplitudes: modular and holomorphic graph functions. We focus on their analytic properties, we recall the known asymptotic behaviour of modular graph functions and we refine the formula for the asymptotic behaviour of holomorphic graph functions. Moreover, we give new evidence of a conjecture appeared in [4] which relates these two asymptotic expansions.

Notes

Acknowledgements

We would like to thank KMPB for the organization of this successful conference. Moreover, we would like to thank C. Dupont, O. Schlotterer and M. Tapus̆ković for useful comments on a first draft and J. Brödel and E. Garcia–Failde for their help with the figures. Our research was supported by a French public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH, and by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n. PCOFUND-GA-2013-609102, through the PRESTIGE programme coordinated by Campus France.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute de Physique Théorique (IPHT)Gif-sur-Yvette CedexFrance

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