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

Abstract

We present a new method to evaluate the ${\alpha }^{\prime }$-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.

6 pages, 2 figures, v2: added explanations, removed the appendix, matches published version

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• Two dialects for KZB equations: generating one-loop open-string integrals
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
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• Symmetric Orbifold Theories from Little String Residues
• Advanced tools for basis decompositions of genus-one string integrals
• A construction of single-valued elliptic polylogarithms