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  • 1STAG Research Centre and Mathematical Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.

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We developed a novel method to analyze the alpha-prime expansion of genus-one integrals, revealing the structure of elliptic multiple zeta values. This approach utilizes a differential equation and Picard iteration for open-string calculations.

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Area of Science:

  • String Theory
  • Mathematical Physics

Background:

  • Genus-one integrals are crucial in string theory.
  • Understanding their alpha-prime expansion is complex.
  • Open-string punctures introduce unique challenges.

Purpose of the Study:

  • To present a new method for evaluating the alpha-prime expansion of genus-one integrals.
  • To unravel the structure of elliptic multiple zeta values in coefficients.
  • To connect genus-one integrals to genus-zero integrals.

Main Methods:

  • Developing a Knizhnik-Zamolodchikov-Bernard-type differential equation for generating functions.
  • Solving the differential equation using Picard iteration.
  • Reducing the initial condition to genus-zero integrals.

Main Results:

  • A novel method for evaluating alpha-prime expansion of genus-one integrals is presented.
  • The structure of elliptic multiple zeta values in the coefficients is elucidated.
  • A connection between genus-one and genus-zero integrals is established.

Conclusions:

  • The proposed method provides a systematic way to study genus-one integrals.
  • This work advances the understanding of elliptic multiple zeta values in string theory.
  • The findings facilitate computations in perturbative string theory.