Identities among higher genus modular graph tensors

Authors: Eric D'Hoker, Oliver Schlotterer

Preprint number: UUITP-36/20

Higher genus modular graph tensors map Feynman graphs to functions on the Torelli space of genus-h compact Riemann surfaces which transform as tensors under the modular group Sp(2h,Z), thereby generalizing a construction of Kawazumi. An infinite family of algebraic identities between one-loop and tree-level modular graph tensors are proven for arbitrary genus and arbitrary tensorial rank.