Black Hole Attractors and Pure Spinors

TL;DR

This paper develops a framework for black hole attractor solutions in N=2 compactifications using pure spinor techniques, accommodating non-Kaehler manifolds and fluxes, extending the classical Calabi-Yau case.

Contribution

It introduces a pure spinor-based formalism for black hole attractors applicable to a broad class of compactifications beyond Calabi-Yau manifolds.

Findings

Attractor equations relate charges to pure spinors in generalized geometry.

The formalism includes non-Kaehler and flux compactifications.

Special case reduces to known Calabi-Yau attractor equations.

Abstract

We construct black hole attractor solutions for a wide class of N=2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to sum_k f_k = Im(C Phi), where Phi is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, Phi=Omega and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.