Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes

TL;DR

This paper develops a novel BRST quantization framework for supersymmetric particle models on quaternionic Kähler manifolds, revealing new geometric structures and connections to black hole physics and cohomology theories.

Contribution

It introduces a BRST detour complex approach to quantize spinning particles in quaternionic Kähler spaces, generalizing quaternionic Dolbeault cohomology and linking to N=2 supergravity black holes.

Findings

Constructed a nilpotent BRST charge using local supersymmetry ghosts.

Discovered a new Dirac operator on superghost extended Hilbert space.

Related Baston's quaternionic cohomology to BPS black hole sectors.

Abstract

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N= 2 supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kaehler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generating special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston's complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kaehler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.