Real weights, bound states and duality orbits

TL;DR

This paper analyzes the duality orbits of extremal black holes in supergravity by examining stabilizing subalgebras and weight vectors, revealing how orbit stratification depends on the properties of these weights across various theories.

Contribution

It provides a unified framework for deriving duality orbits using weight vectors and stabilizers, connecting previous results across different supergravity theories.

Findings

Orbit stratification depends on the nature of weights (real, complex, different lengths).

Maximally non-compact symmetry groups have all real weights, affecting orbit structure.

The approach retrieves and unifies various known results in supergravity black hole classifications.

Abstract

We show that the duality orbits of extremal black holes in supergravity theories with symmetric scalar manifolds can be derived by studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the duality symmetry group. The weight vectors always correspond to weights that are real, where the reality properties are derived from the Tits-Satake diagram that identifies the real form of the Lie algebra of the duality symmetry group. Both N=2 magic Maxwell-Einstein supergravities and the semisimple infinite sequences of N=2 and N=4 theories in D=4 and 5 are considered, and various results, obtained over the years in the literature using different methods, are retrieved. In particular, we show that the stratification of the orbits of these theories occurs because of very specific properties of the representations: in the case of the theory based on the real numbers, whose symmetry group is maximally non-compact and therefore all the weights are real, the stratification is due to the presence of weights of different length, while in the other cases it is due to the presence of complex weights.