English

Two dialects for KZB equations: generating one-loop open-string integrals

High Energy Physics - Theory 2020-12-30 v2 Number Theory

Abstract

Two different constructions generating the low-energy expansion of genus-one configuration-space integrals appearing in one-loop open-string amplitudes have been put forward in \rcites{Mafra:2019xms, *Mafra:2019ddf, Broedel:2019gba}. We are going to show that both approaches can be traced back to an elliptic system of Knizhnik--Zamolodchikov--Bernard(KZB) type on the twice-punctured torus. We derive an explicit all-multiplicity representation of the elliptic KZB system for a vector of iterated integrals with an extra marked point and explore compatibility conditions for the two sets of algebra generators appearing in the two differential equations.

Cite

@article{arxiv.2007.03712,
  title  = {Two dialects for KZB equations: generating one-loop open-string integrals},
  author = {Johannes Broedel and André Kaderli and Oliver Schlotterer},
  journal= {arXiv preprint arXiv:2007.03712},
  year   = {2020}
}

Comments

54 pages, several appendices, corrected typos, updated references

R2 v1 2026-06-23T16:55:52.526Z