Poisson equation for genus two string invariants: a conjecture

Abstract

We consider some string invariants at genus two that appear in the analysis of the $D^8{\mathcal{R}}^4$ and $D^6{\mathcal{R}}^5$ interactions in type II string theory. We conjecture a Poisson equation involving them and the Kawazumi--Zhang invariant based on their asymptotic expansions around the non--separating node in the moduli space of genus two Riemann surfaces.

14 pages, LaTeX; 3 figures

References in corpus (6)

• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• The One-Loop Five-Graviton Amplitude and the Effective Action
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Generating series of all modular graph forms from iterated Eisenstein integrals
• Tetrahedral modular graph functions
• Integrating simple genus two string invariants over moduli space