An extremal black hole with a unique ground state

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.