Related Experiment Video
Updated: Dec 25, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
All Order α^{'} Expansion of One-Loop Open-String Integrals.
Carlos R Mafra1, Oliver Schlotterer2
1STAG Research Centre and Mathematical Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
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.
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.
Related Concept Videos
Euler's Formula for Pin-Ended Columns
To calculate the critical load, envision...
Determination of Pi Terms
The theorem indicates that the...
Summation Notation
Binomial Expansion Using Pascal's Triangle
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
π Molecular Orbitals of the Allyl Radical
The allyl systems have identical molecular orbitals but differ in the number of π electrons....

