Journal
NONASSOCIATIVE MATHEMATICS AND ITS APPLICATIONS
Volume 721, Issue -, Pages 1-27Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/conm/721/14497
Keywords
Non-associative algebras; supergravity; super Yang-Mills theory
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Funding
- Schrodinger Fellowship
- Leverhulme Trust
- STFC [ST/P000762/1]
- STFC [ST/P000762/1] Funding Source: UKRI
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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 4x4 magic square at the base in D = 3, a 3x3 square in D = 4, a 2x2 square in D = 6 and Type II supergravity at the apex in D = 10.
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