A. Kaderli, HU

Title: “Glueing of worldsheets using associator equations: a genus-one, open string example”

Abstract: In this talk, I will show how one-loop, open string (partial) amplitudes can be related to tree-level amplitudes by matrix multiplications. The mechanism is based on a class of iterated integrals, genus-one analogues of Selberg integrals, defined on a genus-one Riemann surface which interpolates between one-loop and tree-level amplitudes. These two boundary values can be related by parallel transport using the elliptic KZB associator. This mechanism can geometrically be interpreted as glueing together two external states of a genus-zero worldsheet leading to a genus-one worldsheet with the number of external states reduced by two. Furthermore, it is assumed to constitute a first step in a recursion in the genus of open string interactions, which extends a similar tree-level recursion in the number of external states (arXix:1304.7304) to interactions of higher genus. The focus will be on the mathematical construction of the elliptic KZB associator, the genus one Selberg integrals and the corresponding associator equation, which implements the glueing mechanism.