BPS states in the large N limit

I will discuss a classification of BPS states into monotone versus fortuitous in holographic CFTs, based on their behaviors in the large N limit. A precise definition will be given in terms of supercharge cohomology, but intuitively, monotone BPS states form infinite sequences with increasing rank, while fortuitous ones are singular existences at individual ranks. It will be argued that under the AdS/CFT correspondence, sequences of monotone BPS states are mapped to perturbative excitations and smooth horizonless geometries in AdS. Based on supporting evidence, I will conjecture that in the large N limit, there are exponentially more fortuitous than monotone BPS states, and the former gives the dominant contribution to the black hole entropy. Finally, I will discuss the implications of our studies on the fuzzball program.