Extremal black hole with a unique ground state

Recent computations in gravity suggest that nonsupersymmetric extremal black holes lack any sizeable ground state degeneracy. We confirm this for a D-brane description of nonsupersymmetric four-charge extremal black holes in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="normal">N</a:mi> <a:mo>=</a:mo> <a:mn>8</a:mn> </a:mrow> </a:math> 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 nonzero energy implying the absence of any truly extremal state. Our arguments rely on symmetry and hence should hold in the supergravity regime as well.