All-order alpha'-expansion of one-loop open-string integrals

TL;DR

This paper introduces a novel method to compute the alpha'-expansion of one-loop open-string integrals using a differential equation approach, revealing the structure of elliptic multiple zeta values in the coefficients.

Contribution

It develops a differential equation framework for evaluating genus-one open-string integrals and connects elliptic multiple zeta values to genus-zero integrals.

Findings

Derived a simple differential equation of KZB-type for the integrals.

Solved the equation via Picard iteration to obtain the alpha'-expansion.

Unveiled the structure of elliptic multiple zeta values in the coefficients.

Abstract

We present a new method to evaluate the $\alpha'$-expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of Knizhnik-Zamolodchikov-Bernard-type satisfied by generating functions of such integrals, and solving it via Picard iteration. The initial condition involves the generating functions at the cusp $\tau\to i\infty$ and can be reduced to genus-zero integrals.