Black-Hole Attractors in N=1 Supergravity

TL;DR

This paper investigates the attractor mechanism in N=1 supergravity theories, deriving equations that depend on the vector multiplet kinetic matrix and exploring models with various duality properties, including connections to pure spinor theory.

Contribution

It derives the attractor equations for N=1 supergravity coupled to matter and explores solutions based on the structure of the kinetic matrix and duality groups.

Findings

Attractor equations depend on the holomorphic symmetric matrix f_{\Lambda\Sigma}

Models with different electric-magnetic duality groups exhibit varied attractor behaviors

Certain models relate attractor equations to pure spinor theory

Abstract

We study the attractor mechanism for N=1 supergravity coupled to vector and chiral multiplets and compute the attractor equations of these theories. These equations may have solutions depending on the choice of the holomorphic symmetric matrix f_{\Lambda\Sigma} which appears in the kinetic lagrangian of the vector sector. Models with non trivial electric-magnetic duality group which have or have not attractor behavior are exhibited. For a particular class of models, based on an N=1 reduction of homogeneous special geometries, the attractor equations are related to the theory of pure spinors.