Modular and holomorphic graph function from superstring amplitudes

TL;DR

This paper compares modular and holomorphic graph functions from superstring amplitudes, analyzing their properties, asymptotics, and a conjectured relation between their expansions, advancing understanding of their mathematical structure.

Contribution

It refines the asymptotic formulas for holomorphic graph functions and provides new evidence supporting a conjecture linking their asymptotics to modular graph functions.

Findings

Refined asymptotic formula for holomorphic graph functions

Confirmed conjectural relation between asymptotic expansions

Enhanced understanding of superstring amplitude functions

Abstract

We compare two classes of functions arising from genus-one superstring amplitudes: modular and holomorphic graph functions. We focus on their analytic properties, we recall the known asymptotic behaviour of modular graph functions and we refine the formula for the asymptotic behaviour of holomorphic graph functions. Moreover, we give new evidence of a conjecture which relates these two asymptotic expansions.