Yang-Mills Theory and the ABC Conjecture
Abstract
We establish a precise correspondence between the ABC Conjecture and N=4 super-Yang-Mills theory. This is achieved by combining three ingredients: (i) Elkies' method of mapping ABC-triples to elliptic curves in his demonstration that ABC implies Mordell/Faltings; (ii) an explicit pair of elliptic curve and associated Belyi map given by Khadjavi-Scharaschkin; and (iii) the fact that the bipartite brane-tiling/dimer model for a gauge theory with toric moduli space is a particular dessin d'enfant in the sense of Grothendieck. We explore this correspondence for the highest quality ABC-triples as well as large samples of random triples. The Conjecture itself is mapped to a statement about the fundamental domain of the toroidal compactification of the string realization of N=4 SYM.
Cite
@article{arxiv.1602.01780,
title = {Yang-Mills Theory and the ABC Conjecture},
author = {Yang-Hui He and Zhi Hu and Malte Probst and James Read},
journal= {arXiv preprint arXiv:1602.01780},
year = {2017}
}
Comments
54+1 pages, 7 figures