Cite as: doi:10.26081/K6632H

**
It has been argued in the past that black holes can carry quantum hair on top
of their mass, electric or magnetic charge, and angular momentum. A
first-principles realization of this idea seems to be emerging in the context
of 1/16 BPS black holes in AdS_5/CFT_4. For large enough charges, we find that
the entropy of the 1/16 BPS sector of the CFT_4, which is SU(N) N=4 SYM,
matches the event horizon area of the classical black hole and quantum
corrections disappear. For small enough charges, though, the area law receives
quantum corrections from complex saddles of the relevant Euclidean partition
function. Some of these saddles happen to be classified by subgroups of
Z_N\times Z_N. Being N the rank of a gauge group, it is natural to expect
that, but not yet understood if, they carry discrete gauge charges, just as
quantum hair should. This talk will review how the previous notion of quantum
corrections to entropy, reminiscent of an effect due to the superposition of
quantum hairs, emerges from a recent first-principles analysis in the context
of a 1/16 BPS twist of AdS/CFT duality, specifically from the analysis of a
unitary matrix integral representation of the partition function of a 1/16 BPS
twist of SU(N) 4d N=4 SYM, at large N.
**

**
**

To download: Right-click and choose "Save Link As..."