A magic square from Yang-Mills squared

TL;DR

This paper unifies various three-dimensional super-Yang-Mills theories using division algebras and constructs a magic square framework that relates these gauge theories to supergravity models with different supersymmetries.

Contribution

It introduces a unified algebraic description of D=3 super-Yang-Mills theories via division algebras and constructs a magic square linking these theories to supergravity with various supersymmetries.

Findings

Unified description of super-Yang-Mills theories using division algebras.

Construction of a magic square relating gauge theories to supergravity.

Explicit correspondence between algebraic structures and supersymmetry levels.

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.