A Farey tale for N=4 dyons

Understand

We study exponentially suppressed contributions to the degeneracies of extremal black holes.

• Within Sen's quantum entropy function framework and focusing on extremal black holes with an intermediate AdS3 region, we identify an infinite family of semi-classical AdS2 geometries which can contribute effects of order exp(S_0/c), where S_0 is the Bekenstein-Hawking-Wald entropy and c is an integer greater than one.
• These solutions lift to the extremal limit of the SL(2,Z) family of BTZ black holes familiar from the "black hole Farey tail".
• We test this understanding in N=4 string vacua, where exact dyon degeneracies are known to be given by Fourier coefficients of Siegel modular forms.