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(16.07.) Bases and differential equations for one-loop string integrals

Oliver Schlotterer (Uppsala)

16.07.2020 at 16:15 

The goal of this talk is to describe an organizing principle for string amplitudes and their low-energy expansions, where the moduli-space integrals over punctured worldsheets are cast into a basis. In order to motivate and illustrate the strategy, I will review the tree-level bases of n-point open-string integrals over the disk boundary and closed-string integrals over the sphere. At one loop, similar sets of integrals over the cylinder boundary and the torus will be introduced as a
conjectural basis at genus one. On a fixed surface, the genus-one integrals over the punctures are shown to obey first-order differential equations in the modular parameter which determine the number-theoretic properties of the low-energy expansion. More specifically, solving the differential equations via Picard iteration will be shown to efficiently generate the elliptic multiple zeta values in the open-string alpha’-expansions and the modular graph forms in their closed-string analogues.

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