An extremal black hole with a unique ground state

TL;DR

This paper confirms that non-supersymmetric extremal black holes in N=8 string theory have a unique ground state with no degeneracy, supported by a D-brane microscopic description and low-energy analysis.

Contribution

It provides a detailed D-brane worldline Lagrangian for non-supersymmetric 4-charge extremal black holes, showing the absence of ground state degeneracy.

Findings

Hamiltonian has a unique ground state with non-zero energy

Low energy worldline Lagrangian includes 32 Goldstinos and 28 Goldstones

Supports the idea that such black holes lack sizeable ground state degeneracy

Abstract

Recent computations in gravity suggest that non-supersymmetric extremal black holes lack any sizeable ground state degeneracy. We confirm this for D-brane description of non-supersymmetric 4-charge extremal black holes in N=8 string theory. The microscopic description comprises four stacks of D-branes wrapping various cycles of the internal six-torus and intersecting at a point. The orientations of the stacks are such that supersymmetry is broken completely. We construct the low energy worldline Lagrangian for the brane system, which is seen to have 32 Goldstinos and 28 Goldstones. The Hamiltonian has a unique ground state, which carries a non-zero energy implying the absence of any truly extremal state.