On N=8 attractors

TL;DR

This work provides a unified framework to derive and solve the attractor equations for $N=8$ supergravity by extending the $N=2$ special-geometry (symplectic) structure to all $N>2$ and formulating a compact algebraic condition for the fixed scalars at the black hole horizon. It identifies two regular attractor classes—1/8 BPS and non-BPS—each with explicit expressions for the quartic invariant $J_4$ and horizon entropy, and demonstrates how the $N=8$ problem maps onto an embedded $N=2$ STU sector, clarifying the stabilization mechanism. The STU interpretation provides a concrete bridge to lower-supersymmetry theories, showing how the $SO^*(12)/U(6)$ sector captures 32 charges while remaining 40 scalars remain unfixed, and connects the attractor physics to invariant constructions in quantum information theory, including GHZ-type charge configurations. Overall, the paper gives a tractable set of algebraic attractor equations for $N=8$ and reveals deep connections between black hole physics, duality symmetries, and information-theoretic structures.

Abstract

We derive and solve the black hole attractor conditions of N=8 supergravity by finding the critical points of the corresponding black hole potential. This is achieved by a simple generalization of the symplectic structure of the special geometry to all extended supergravities with $N>2$. There are two solutions for regular black holes, one for 1/8 BPS ones and one for the non-BPS. We discuss the solutions of the moduli at the horizon for BPS attractors using N=2 language. An interpretation of some of these results in N=2 STU black hole context helps to clarify the general features of the black hole attractors.