Identities among higher genus modular graph tensors

Abstract

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 $Sp(2h,\mathbb{Z})$, 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. We also derive a family of identities that apply to modular graph tensors of higher loop order.

37 pages, v2: added a few figures and explanations; version to appear in Communications in Number Theory and Physics

References in corpus (4)

• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Johnson's homomorphisms and the Arakelov-Green function
• Poisson equations for elliptic modular graph functions
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors

Cited by in corpus (2)

• Relations between elliptic modular graphs
• Integrating simple genus two string invariants over moduli space