A Generalisation of (Very) Special Geometry

TL;DR

This paper extends the understanding of special geometry in supersymmetric theories by constructing non-Abelian N=2 vector multiplets in 4D and 5D, revealing broader geometric structures and potentials beyond traditional models.

Contribution

It introduces a framework for non-Abelian N=2 vector multiplets with on-shell closure, broadening the class of target-space geometries and potentials in supersymmetric theories.

Findings

Broader class of target-space geometries identified.

Inclusion of Fayet-Iliopoulos terms in non-Abelian theories.

Relation between 4D and 5D theories via dimensional reduction.

Abstract

We construct non-Abelian N=2 on-shell vector multiplets in five and in four dimensions. Closing of the supersymmetry algebra imposes dynamical constraints on the fields, and these constraints should be interpreted as equations of motion. If these field equations should not be derivable from an action, we find that supersymmetry allows a broader class of target-space geometries than the familiar rigid (very) special manifolds. These theories moreover have more general potentials due to the possibility of including Fayet-Iliopoulos terms in the non-Abelian case. We show that by introducing an action, we recover the standard results. Finally, we relate the five- and the four-dimensional theories through dimensional reduction and discuss the corresponding generalised r-map.