English

A magic square from Yang-Mills squared

High Energy Physics - Theory 2015-01-08 v3 Rings and Algebras

Abstract

We give a unified description of D = 3 super-Yang-Mills theory with N = 1, 2, 4, and 8 supersymmeties in terms of the four division algebras: reals (R), complexes (C), quaternions (H) and octonions (O). Tensoring left and right super-Yang-Mills multiplets with N = 1, 2, 4, 8 we obtain a magic square RR, CR, CC, HR, HC, HH, OR, OC, OH, OO description of D = 3 supergravity with N = 2, 3, 4, 5, 6, 8, 9, 10, 12, 16.

Cite

@article{arxiv.1301.4176,
  title  = {A magic square from Yang-Mills squared},
  author = {L. Borsten and M. J. Duff and L. J. Hughes and S. Nagy},
  journal= {arXiv preprint arXiv:1301.4176},
  year   = {2015}
}

Comments

4 pages, refs 11 and 12 added, footnote 1 modified. Updated to match published version

R2 v1 2026-06-21T23:11:22.860Z