Publication : t15/202

Modular Graph Functions

D Hoker, Eric (Department of Physics and Astronomy, University of California (UCLA), Los Angeles, CA 90095-1547, USA)
Green M.B. (Department of Applied Mathematics and Theoretical Physics (DAMTP), Center for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England UNITED KINGDOM (UK))
gurdogan, o (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Vanhove P. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
We consider properties of modular graph functions, which are non-holomorphic modular functions associated with the Feynman graphs for a conformal scalar field theory on a two-dimensional torus. Such functions arise, for example, in the low energy expansion of genus-one Type II superstring amplitudes. We demonstrate that these functions are sums, with rational coefficients, of special values of single-valued elliptic multiple polylogarithms, which will be introduced in this paper. This insight suggests the many interrelations between these modular graph functions (a few of which were motivated in an earlier paper) may be obtained as a consequence of identities involving elliptic polylogarithms.
Année de publication : 2017
Revue : Commun.Num.Theor.Phys 11 165-218 (2017)
DOI : 10.4310/CNTP.2017.v11.n1.a4
Preprint : arXiv:1512.06779
Langue : Anglais

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