Poisson equations for elliptic modular graph functions

Abstract

We obtain Poisson equations satisfied by elliptic modular graph functions with four links. Analysis of these equations leads to a non--trivial algebraic relation between the various graphs.

17 pages, LaTeX, 9 figures

References in corpus (2)

• Generating series of all modular graph forms from iterated Eisenstein integrals
• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality

Cited by in corpus (9)

• The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals
• Poincaré series for modular graph forms at depth two. II. Iterated integrals of cusp forms
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• Elliptic modular graph forms I: Identities and generating series
• To the cusp and back: Resurgent analysis for modular graph functions
• Relations between elliptic modular graphs
• Identities among higher genus modular graph tensors
• Poisson equation for genus two string invariants: a conjecture
• Integrating simple genus two string invariants over moduli space