Statut  Confirmé 
Série  RENCTHEO 
Domaines  hepth 
Date  Jeudi 5 Octobre 2017 
Heure  10:00 
Institut  IHP 
Salle  314 
Nom de l'orateur  Vanhove 
Prenom de l'orateur  Pierre 
Addresse email de l'orateur  vanhove [dot] pierre [at] gmail [dot] com 
Institution de l'orateur  CEA Saclay 
Titre  The sunset in the mirror: a regulator for inequality in the masses 
Résumé  We study the Feynman integral for the sunset graph defined as the scalar twopoint self energy at twoloop order. The Feynman integral is evaluated for all inequal internal masses in two spacetime dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical PicardFuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of elliptic curves. Using an Hodge theoretic (Bmodel) 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 noncompact CalabiYau 3fold, obtained as a limit of elliptically fibered compact CalabiYau 3folds. By considering the limiting mixed Hodge structure of the Batyrev dual Amodel, we arrive at an expression for the sunset Feynman integral in terms of the local GromovWitten 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 (Based on work done in collaboration with Spencer Bloch and Matt Kerr.) 
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