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Article overview
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Yang-Mills Theory and the ABC Conjecture | | Yang-Hui He
; Zhi Hu
; Malte Probst
; James Read
; | | Date: |
4 Feb 2016 | | 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. | | Source: | arXiv, 1602.1780 | | Services: | Forum | Review | PDF | Favorites | |
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