Jordan Pairs, E6 and U-Duality in Five Dimensions

TL;DR

This paper explores the algebraic structures underlying five-dimensional supergravity theories, revealing how Jordan pairs and U-duality symmetries determine the spectrum and multiplet organization across various models.

Contribution

It introduces a novel analysis connecting Jordan pair structures with U-duality in D=3 and super-Ehlers symmetry in D=5, clarifying the massless multiplet structure in supergravity.

Findings

Identifies the role of Jordan pairs in supergravity spectra

Classifies theories based on Jordan algebra types

Elucidates the relation between algebraic structures and supersymmetry variations

Abstract

By exploiting the Jordan pair structure of U-duality Lie algebras in D = 3 and the relation to the super-Ehlers symmetry in D = 5, we elucidate the massless multiplet structure of the spectrum of a broad class of D = 5 supergravity theories. Both simple and semi-simple, Euclidean rank-3 Jordan algebras are considered. Theories sharing the same bosonic sector but with different supersymmetrizations are also analyzed.