Elliptic multiple zeta values and one-loop superstring amplitudes

Understand

We investigate iterated integrals on an elliptic curve, which are a natural genus-one generalization of multiple polylogarithms.

• These iterated integrals coincide with the multiple elliptic polylogarithms introduced by Brown and Levin when constrained to the real line.
• At unit argument they reduce to an elliptic analogue of multiple zeta values, whose network of relations we start to explore.
• A simple and natural application of this framework are one-loop scattering amplitudes in open superstring theory.