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<p>It has long been known that the maximal cut of the equal-mass four-loop banana integral is a period of a family of Calabi-Yau threefolds that depends on the kinematic variable <i>z</i> = <i>m</i><sup>2</sup>/<i>p</i><sup>2</sup>. We show that it can also be interpreted as a period of a family of genus-two curves. We do this by introducing a general Calabi-Yau-to-curve correspondence, which in this case locally relates the original period of the family of Calabi-Yau threefolds to a period of a family of genus-two curves that varies holomorphically with the kinematic variable <i>z</i>. In addition to working out the concrete details of this correspondence for the equal-mass four-loop banana integral, we outline when we expect a correspondence of this type to hold.</p>

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A Calabi-Yau-to-curve correspondence for Feynman integrals

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月2日

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  • Hans Jockers,
  • Sören Kotlewski,
  • Pyry Kuusela,
  • Andrew J. McLeod,
  • Sebastian Pögel,
  • Maik Sarve,
  • Xing Wang,
  • Stefan Weinzierl

摘要

It has long been known that the maximal cut of the equal-mass four-loop banana integral is a period of a family of Calabi-Yau threefolds that depends on the kinematic variable z = m2/p2. We show that it can also be interpreted as a period of a family of genus-two curves. We do this by introducing a general Calabi-Yau-to-curve correspondence, which in this case locally relates the original period of the family of Calabi-Yau threefolds to a period of a family of genus-two curves that varies holomorphically with the kinematic variable z. In addition to working out the concrete details of this correspondence for the equal-mass four-loop banana integral, we outline when we expect a correspondence of this type to hold.