HKT and OKT Geometries on Soliton Black Hole Moduli Spaces

TL;DR

This paper explores the geometric structures of black hole moduli spaces, revealing hyper-Kähler with torsion and octonionic-Kähler with torsion geometries, and connects these to brane configurations and supersymmetric models.

Contribution

It demonstrates that certain black hole moduli spaces have hyper-Kähler with torsion and octonionic-Kähler with torsion geometries, linking them to extended supersymmetry and brane interpretations.

Findings

Moduli space geometries are hyper-Kähler with torsion and octonionic-Kähler with torsion.

These geometries naturally arise from extended world-line supersymmetry models.

A broad class of such geometries is constructed across various dimensions.

Abstract

We consider Shiraishi's metrics on the moduli space of extreme black holes. We interpret the simplification in the pattern of N-body interactions that he observed in terms of the recent picture of black holes in four and five dimensions as composites, made up of intersecting branes. We then show that the geometry of the moduli space of a class of black holes in five and nine dimensions is hyper-K\"ahler with torsion, and octonionic-K\"ahler with torsion, respectively. For this, we examine the geometry of point particle models with extended world-line supersymmetry and show that both of the above geometries arise naturally in this context. In addition, we construct a large class of hyper-K\"ahler with torsion and octonionic-K\"ahler with torsion geometries in various dimensions. We also present a brane interpretation of our results.