Séminaire de Mathématiques de l'Institut de Physique Théorique du CEA-Saclay

# Axel Kleinschmidt: Towards a single-valued map at genus one

Europe/Paris
Zoom Meeting ID: 264 969 3492 Passwords: sent to participants by email the day before the seminar via the mailing list.
Description

Axel Kleinschmidt

Towards a single-valued map at genus one

Closed string amplitudes at genus one can be described in terms of modular graph forms. These real-analytic functions with definite transformation properties under SL(2,$\mathbb{Z}$) can be represented either as lattice sums over world-sheet torus momenta or as configuration space integrals. It is convenient to package them into a generating series involving Kronecker-Eisenstein series and a Koba-Nielsen factor. The generating series can be shown to satisfy a differential equation that contains a (conjectural) matrix representation of Tsunogai's derivation algebra and whose formal solution involves iterated Eisenstein integrals as studied by Brown. The closed string differential equation can be viewed as a single-valued version of a corresponding open string equation and, together with the input of the genus zero single-valued map in the form of initial conditions, this suggests a candidate genus one single-valued map.

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This is the page for the online seminar on motives and period integrals in Quantum field theory and String theory.

The seminars will solely take place online

Zoom Meeting ID: 264 969 3492
Passwords: sent to participants by email the day before the seminar via the mailing list.
If you are interested in joigning this seminar series you should contact the organisers.

Organized by

Pierre Vanhove and Federico Zerbini