Poisson equation for genus two string invariants: a conjecture

TL;DR

This paper proposes a conjecture relating genus two string invariants and the Kawazumi--Zhang invariant through a Poisson equation, based on their asymptotic behavior in string theory interactions.

Contribution

It introduces a new conjecture connecting string invariants and the Kawazumi--Zhang invariant via a Poisson equation, advancing understanding of genus two Riemann surfaces in string theory.

Findings

Conjectured a Poisson equation involving genus two string invariants.

Linked string invariants to the Kawazumi--Zhang invariant.

Based on asymptotic expansions around the non-separating node.

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.