AdS black holes and finite N indices

Understand

We study the index of 4d $\mathcal{N}=4$ Yang-Mills theory with $U(N)$ gauge group, focussing on the physics of the dual BPS black holes in $AdS_5\times S^5$.

• Certain aspects of these black holes can be studied from finite $N$ indices with reasonably large $N^2$.
• We make numerical studies of the index for $N\leq 6$, by expanding it up to reasonably high orders in the fugacity.
• The entropy of the index agrees very well with the Bekenstein-Hawking entropy of the dual black holes, say at $N^2=25$ or $36$.