Orbits in Non-Supersymmetric Magic Theories

TL;DR

This paper classifies electric-magnetic duality orbits of fluxes supporting extremal black branes in non-supersymmetric magic theories, revealing a single orbit per non-maximal rank element, similar to maximal supergravity.

Contribution

It provides a detailed classification of duality orbits in non-supersymmetric magic Maxwell-Einstein theories, extending understanding from maximal supergravity.

Findings

Only one orbit per non-maximal rank element in each dimension.

No splitting of orbits occurs in these theories.

Results relate to Jordan algebras and Freudenthal systems.

Abstract

We determine and classify the electric-magnetic duality orbits of fluxes supporting asymptotically flat, extremal black branes in $D=4,5,6$ space-time dimensions in the so-called non-supersymmetric magic Maxwell-Einstein theories, which are consistent truncations of maximal supergravity and which can be related to Jordan algebras (and related Freudenthal triple systems) over the split complex numbers $\mathbb{C}_{s}$ and the split quaternions $\mathbb{H}_{s}$. By studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the electric-magnetic duality symmetry group, we obtain that, as for the case of maximal supergravity, in magic non-supersymmetric Maxwell-Einstein theories there is no splitting of orbits, namely there is only one orbit for each non-maximal rank element of the relevant Jordan algebra (in $D=5$ and $6$) or of the relevant Freudenthal triple system (in $D=4$).