Skip to main content

Research Repository

Advanced Search

ADHM polytopes

Allen, James; Sutcliffe, Paul

ADHM polytopes Thumbnail


James Allen


We discuss the construction of ADHM data for Yang-Mills instantons with the symmetries of the regular polytopes in four dimensions. We show that the case of the pentatope can be studied using a simple modification of the approach previously developed for platonic data. For the remaining polytopes, we describe a framework in which the building blocks of the ADHM data correspond to the edges in the extended Dynkin diagram that arises via the McKay correspondence. These building blocks are then assembled into ADHM data through the identification of pairs of commuting representations of the associated binary polyhedral group. We illustrate our procedure by the construction of ADHM data associated with the pentatope, the hyperoctahedron and the 24-cell, with instanton charges 4, 7 and 23, respectively. Furthermore, we show that within our framework these are the lowest possible charges with these symmetries. Plots of topological charge densities are presented that confirm the polytope structucore and the relation to JNR instanton data is clarified.


Allen, J., & Sutcliffe, P. (2013). ADHM polytopes. Journal of High Energy Physics, 2013(5), Article 63.

Journal Article Type Article
Publication Date May 14, 2013
Deposit Date Jun 10, 2013
Publicly Available Date Jun 14, 2013
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2013
Issue 5
Article Number 63
Keywords Solitons monopoles and instantons, Discrete and finite symmetries.


Accepted Journal Article (1.4 Mb)

Copyright Statement
© SISSA 2013. Published by Springer on behalf of International School for Advanced Studies (SISSA - Trieste, Italy). The final publication is available at Springer via

You might also like

Downloadable Citations