Modular forms in Quantum Field Theory
Algebraic Geometry
2013-06-28 v2 High Energy Physics - Theory
Abstract
The amplitude of a Feynman graph in Quantum Field Theory is related to the point-count over finite fields of the corresponding graph hypersurface. This article reports on an experimental study of point counts over F_q modulo q^3, for graphs up to loop order 10. It is found that many of them are given by Fourier coefficients of modular forms of weights <=8 and levels <=17.
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Cite
@article{arxiv.1304.5342,
title = {Modular forms in Quantum Field Theory},
author = {Francis Brown and Oliver Schnetz},
journal= {arXiv preprint arXiv:1304.5342},
year = {2013}
}
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27 pages