The mile high magic pyramid

A. Anastasiou, L. Borsten, M. J. Duff, A. Marrani, S. Nagy, M. Zoccali

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Citations (Scopus)


. Using a unified formulation of N = 1, 2, 4, 8, super Yang-Mills theories in D = 3 spacetime dimensions with fields valued respectively in R, C, H, O, it was shown that tensoring left and right multiplets yields a Freudenthal magic square of D = 3 supergravities. When tied in with the more familiar R, C, H, O description of super Yang-Mills in D = 3, 4, 6, 10 this results in a magic pyramid of supergravities: the known 4 × 4 magic square at the base in D = 3, a 3 × 3 square in D = 4, a 2 × 2 square in D = 6 and Type II supergravity at the apex in D = 10.

Original languageEnglish
Title of host publicationNonassociative Mathematics and its Applications
EditorsPetr Vojtechovský, Murray R. Bremner, J. Scott Carter, Anthony B. Evans, John Huerta, Michael K. Kinyon, G. Eric Moorhouse, Jonathan D.H. Smith
PublisherAmerican Mathematical Society
Number of pages27
ISBN (Print)9781470442453
Publication statusPublished - 2019
Event4th Mile High Conference on Nonassociative Mathematics, 2017 - Denver, United States
Duration: 29 Jul 20175 Aug 2017

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


Conference4th Mile High Conference on Nonassociative Mathematics, 2017
Country/TerritoryUnited States


  • Non-associative algebras
  • Super Yang-Mills theory
  • Supergravity


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