Supersymmetry and Attractors in N = 4 Supergravity: The Superconformal Approach

Abstract

In this paper, we study the attractor mechanism for extremal, spherically symmetric black holes in pure, untruncated, N=4 Poincaré supergravity, which we demonstrate numerically. We further study the supersymmetries preserved by these attractor solutions by focussing specifically on the constant moduli solutions and show that they always preserve 1/4$^{th}$ of the total supersymmetries. We also give an argument that even the attractor solutions with a ``non-constant'' moduli would preserve 1/4$^{th}$ of the total supersymmetries. This would mean that in pure N=4 supergravity there exist no attractor solutions which are non-supersymmetric although they could in-principle exist in a matter coupled theory. We use the framework of conformal supergravity in our analysis, which is a manifestly off-shell framework and considerably simplifies the Killing spinor analysis.