SL(5) supersymmetry

TL;DR

This paper explores supersymmetry in five dimensions with fermionic parameters as 2-forms under SL(5), revealing deep algebraic structures and relationships among various infinite-dimensional superalgebras.

Contribution

It introduces a pure spinor superfield formalism for 5D supersymmetry and establishes connections between supermultiplets and advanced algebraic extensions.

Findings

Supermultiplets are linked to Borcherds superalgebra, tensor hierarchy algebra, and exceptional superalgebra.

A theorem relates these algebras to all levels, revealing their structural connections.

The formalism advances understanding of supersymmetry algebra extensions in higher dimensions.

Abstract

We consider supersymmetry in five dimensions, where the fermionic parameters are a 2-form under SL(5). Supermultiplets are investigated using the pure spinor superfield formalism, and are found to be closely related to infinite-dimensional extensions of the supersymmetry algebra: the Borcherds superalgebra ${\scr B}(E_4)$, the tensor hierarchy algebra $S(E_4)$ and the exceptional superalgebra $E(5,10)$. A theorem relating ${\scr B}(E_4)$ and $E(5,10)$ to all levels is given.