Publication : t15/135

Local mirror symmetry and the sunset Feynman integral

Bloch S. (University of Chicago)
kerr, m (Department of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis, MO 63130-4899, USA)
Vanhove P. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
We study the sunset Feynman integral defined as the scalar two-point self-energy at two-loop order in a two dimensional space-time.
We firstly compute the Feynman integral, for arbitrary internal masses, in terms of the regulator of a class in the motivic cohomology of a 1-parameter family of open elliptic curves. Using an Hodge theoretic (B-model) approach, we show that the integral is given by a sum of elliptic dilogarithms evaluated at the divisors determined by the punctures.
Secondly we associate to the sunset elliptic curve a local non-compact Calabi-Yau 3-fold, obtained as a limit of elliptically fibered compact Calabi-Yau 3-folds. By considering the limiting mixed Hodge structure of the Batyrev dual A-model, we arrive at an expression for the sunset Feynman integral in terms of the local Gromov-Witten prepotential of the del Pezzo surface of degree 6. This expression is obtained by proving a strong form of local mirror symmetry which identifies this prepotential with the second regulator period of the motivic cohomology class.
Année de publication : 2017
Revue : Adv. Theor. Math. Phys. 21 1373-1453 (2017)
DOI : 10.1016/j.jnt.2017.07.022
Preprint : arXiv:1601.08181
Langue : Anglais


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