On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds

TL;DR

This paper analyzes the structure of moduli spaces for non-BPS extremal black hole attractors in N=2 supergravity, revealing their geometric properties and differences based on central charge conditions.

Contribution

It characterizes the moduli spaces of non-BPS attractors in N=2 symmetric manifolds, linking them to special and homogeneous symmetric geometries, and explores their relation to five-dimensional theories.

Findings

Non-BPS attractors with non-zero central charge have moduli spaces described by real special geometry.

Non-BPS attractors with zero central charge have moduli spaces as Kahler homogeneous symmetric manifolds.

Moduli spaces of related N=2, d=5 theories are rank-1 homogeneous symmetric manifolds.

Abstract

We study the ``flat'' directions of non-BPS extremal black hole attractors for N=2, d=4 supergravities whose vector multiplets' scalar manifold is endowed with homogeneous symmetric special Kahler geometry. The non-BPS attractors with non-vanishing central charge have a moduli space described by real special geometry (and thus related to the d=5 parent theory), whereas the moduli spaces of non-BPS attractors with vanishing central charge are certain Kahler homogeneous symmetric manifolds. The moduli spaces of the non-BPS attractors of the corresponding N=2, d=5 theories are also indicated, and shown to be rank-1 homogeneous symmetric manifolds.