New realizations of modular forms in Calabi-Yau threefolds arising from $\phi^4$ theory
Number Theory
2018-10-23 v4 Algebraic Geometry
Abstract
It has been found experimentally by Brown and Schnetz that the number of points over of a graph hypersurface is often related to the coefficients of a modular form. In this paper I prove this relation for one example of a modular form of weight and two of weight , refine the statement and suggest a method of proving it for four more of weight , and use the one proved example to construct two new rigid Calabi-Yau threefolds that realize Hecke eigenforms of weight (one provably and one conjecturally).
Keywords
Cite
@article{arxiv.1604.04918,
title = {New realizations of modular forms in Calabi-Yau threefolds arising from $\phi^4$ theory},
author = {Adam Logan},
journal= {arXiv preprint arXiv:1604.04918},
year = {2018}
}
Comments
Brief note added in separate file, indicating that a condition on which one of the results depends can now be removed, also, journal reference and DOI added. Main file unchanged