Small Orbits

TL;DR

This paper classifies extremal black hole charge orbits in various supergravity theories using cubic Jordan algebras, providing minimal charge representatives, stabilizers, and moduli spaces across multiple models and dimensions.

Contribution

It introduces a unified formalism based on cubic Jordan algebras to systematically analyze charge orbits in diverse supergravity theories, including novel treatments for specific models.

Findings

Derived minimal charge representatives for various models.

Identified stabilizer groups and moduli spaces for charge orbits.

Unified classification framework applicable to multiple supergravity theories.

Abstract

We study both the "large" and "small" U-duality charge orbits of extremal black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan algebras and their associated Freudenthal triple systems, in order to derive the minimal charge representatives, their stabilizers and the associated "moduli spaces". After recalling N = 8 maximal supergravity, we consider N = 2 and N = 4 theories coupled to an arbitrary number of vector multiplets, as well as N = 2 magic, STU, ST^2 and T^3 models. While the STU model may be considered as part of the general N = 2 sequence, albeit with an additional triality symmetry, the ST^2 and T^3 models demand a separate treatment, since their representative Jordan algebras are Euclidean or only admit non-zero elements of rank 3, respectively. Finally, we also consider minimally coupled N = 2, matter coupled N = 3, and "pure" N = 5 theories.