E(7) Symmetric Area of the Black Hole Horizon

TL;DR

This paper explores the properties of black hole horizons in N=8 supergravity, revealing that the horizon area is linked to E7(7) symmetry and is protected by non-renormalization theorems, especially for extremal black holes with specific supersymmetry.

Contribution

It demonstrates that the horizon area in N=8 supergravity is proportional to the E7(7) invariant quartic form and is non-zero only for certain supersymmetry fractions, highlighting symmetry protection.

Findings

Horizon area is proportional to the E7(7) invariant quartic form.

Area vanishes when 1/4 or 1/2 supersymmetry is unbroken.

Non-renormalization theorem protects the horizon area in N=8 supergravity.

Abstract

Extreme black holes with 1/8 of unbroken N=8 supersymmetry are characterized by the non-vanishing area of the horizon. The central charge matrix has four generic eigenvalues. The area is proportional to the square root of the invariant quartic form of $E_{7(7)}$. It vanishes in all cases when 1/4 or 1/2 of supersymmetry is unbroken. The supergravity non-renormalization theorem for the area of the horizon in N=8 case protects the unique U-duality invariant.