Monodromy relations from twisted homology

Understand

We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus.

• This allows us to write explicit linear relations involving loop integrands of open-string theories for any number of external particles and, for the first time, to arbitrary genus.
• In the non-planar sector, these relations contain seemingly unphysical contributions, which we argue clarify mismatches in previous literature.
• The text is mostly self-contained and presents a concise introduction to twisted homologies.