The Mile High Magic Pyramid

TL;DR

This paper unifies super Yang-Mills theories across various dimensions and division algebras to construct a hierarchical pyramid of supergravity theories, revealing deep algebraic structures connecting different spacetime dimensions.

Contribution

It introduces a unified framework linking super Yang-Mills theories with division algebras to generate a supergravity pyramid across dimensions.

Findings

Constructed a supergravity pyramid from super Yang-Mills theories.

Connected division algebras to supergravity structures.

Revealed algebraic patterns underlying supergravity in various dimensions.

Abstract

Using a unified formulation of $\mathcal{N} = 1, 2, 4, 8$, super Yang-Mills theories in $D = 3$ spacetime dimensions with fields valued respectively in $\mathbb{R, C, H, O}$, 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 $\mathbb{R, C, H, O}$ description of super Yang-Mills in $D = 3, 4, 6, 10$ this results in a magic pyramid of supergravities: the known $4 \times 4$ magic square at the base in $D=3$, a $3\times 3$ square in $D=4$, a $2 \times 2$ square in $D=6$ and Type II supergravity at the apex in $D=10$.