Abstract
We study nearly extreme black holes with nearly AdS2 horizon geometry in various settings inspired by string theory. Our focus is on the scales of the nAdS2 region and their relation to microscopic theory. These scales are determined by a generalization of the attractor mechanism for extremal black holes and realized geometrically as the normal derivatives along the extremal attractor flow. In some cases the scales are equivalently determined by the charge dependence of the extremal attractor by itself. Our examples include near extreme black holes in D ≥ 4 dimensions, AdS boundary conditions, rotation, and 5D black holes on the non-BPS branch.
Highlights
The holographic correspondence between nearly AdS2 geometry and nearly CFT1’s [1,2,3] is not conformal
We study nearly extreme black holes with nearly AdS2 horizon geometry in various settings inspired by string theory
Both sides of the duality depend on a scale and for both it is natural to focus on effective quantum field theory near the IR
Summary
The holographic correspondence between nearly AdS2 geometry and nearly CFT1’s [1,2,3] is not conformal. The radial derivative probes the extremal geometry infinitesimally beyond the AdS2 horizon region This is satisfying from an effective quantum field theory point of view because this simple device realizes geometrically the determination of the IR scale by matching with the UV data embodied in the attractor flow (radial dependence). The extremal attractor mechanism determines the value of these scalars at the horizon in terms of black hole charges while the nAttractor mechanism gives a (complex) scale analogous to (1.3) for each scalar These other scales are the dimensionful couplings entering the boundary theory describing vector fields in nAdS2 [26,27,28].
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