arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1602.01780hep-thmath.NT
收藏

Yang-Mills理论与ABC猜想

Yang-Mills Theory and the ABC Conjecture

Yang-Hui He, Zhi Hu, Malte Probst, James Read

摘要:

我们建立了ABC猜想与N=4超杨-米尔斯理论之间的精确对应。这是通过结合三个成分实现的:(i)Elkies的方法映射ABC-三元组椭圆曲线在他的示范,ABC意味着莫德尔/法尔丁斯;(ii)一个明确的椭圆曲线对和相关的Belyi映射给出的Khadjavi-Scharaschkin;和(iii)的事实,即二分膜平铺/二聚体模型的规范理论与环面模空间是一个特殊的dessin d 'enfant在格罗滕迪克的意义。我们探索这种对应关系的最高质量的ABC三元组以及随机三元组的大样本。猜想本身被映射到一个关于N=4 SYM的弦实现的环形紧化的基本域的陈述。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑