Arithmetic of Quantum Entropy Function

Understand

Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics.

• We show that in N=4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e.
• different arithmetical properties.
• These arise from additional saddle points in the path integral -- whose existence depends on the arithmetical properties of the black hole charges -- constructed as freely acting orbifolds of the original AdS_2\times S^2 near horizon geometry.