Magic square from Yang-Mills squared.

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.