Cover Image

Yang-Mills theory and the ABC conjecture

We establish a precise correspondence between the ABC Conjecture and N=4š¯’©=4<math display="inline" overflow="scroll" altimg="eq-00001.gif"><mi mathvariant="cal">š¯’©</mi><mo class="MathClass-rel">=</mo><mn>4</mn>...

Full description

Saved in:
Bibliographic Details
Main Authors: He, Yang-Hui (Author) , Hu, Zhi (Author) , Probst, Malte (Author) , Read, James (Author)
Format: Article (Journal)
Language:English
Published: 3 May 2018
In: International journal of modern physics. A, Particles and fields, gravitation, cosmology
Year: 2018, Volume: 33, Issue: 13
ISSN:1793-656X
DOI:10.1142/S0217751X18500537
Online Access:Verlag, Volltext: https://doi.org/10.1142/S0217751X18500537
Verlag: https://www.worldscientific.com/doi/abs/10.1142/S0217751X18500537
Get full text
Author Notes:Yang-Hui He, Zhi Hu, Malte Probst and James Read
Description
Summary:We establish a precise correspondence between the ABC Conjecture and N=4š¯’©=4<math display="inline" overflow="scroll" altimg="eq-00001.gif"><mi mathvariant="cal">š¯’©</mi><mo class="MathClass-rel">=</mo><mn>4</mn></math> super-Yang-Mills theory. This is achieved by combining three ingredients: (i) Elkiesā€™ 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 dā€™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=4š¯’©=4<math display="inline" overflow="scroll" altimg="eq-00002.gif"><mi mathvariant="cal">š¯’©</mi><mo class="MathClass-rel">=</mo><mn>4</mn></math> SYM.
Item Description:Gesehen am 22.10.2019
Physical Description:Online Resource
ISSN:1793-656X
DOI:10.1142/S0217751X18500537

Similar Items