From modular forms to differential equations for Feynman integrals
Abstract
In these proceedings we discuss a representation for modular forms that is more suitable for their application to the calculation of Feynman integrals in the context of iterated integrals and the differential equation method. In particular, we show that for every modular form we can find a representation in terms of powers of complete elliptic integrals of the first kind multiplied by algebraic functions. We illustrate this result on several examples. In particular, we show how to explicitly rewrite elliptic multiple zeta values as iterated integrals over powers of complete elliptic integrals and rational functions, and we discuss how to use our results in the context of the system of differential equations satisfied by the sunrise and kite integrals.
Cite
@article{arxiv.1807.00842,
title = {From modular forms to differential equations for Feynman integrals},
author = {Johannes Broedel and Claude Duhr and Falko Dulat and Brenda Penante and Lorenzo Tancredi},
journal= {arXiv preprint arXiv:1807.00842},
year = {2018}
}
Comments
Contribution to "Elliptic integrals, elliptic functions and modular forms in quantum field theory"