Black hole entropy function for toric theories via Bethe Ansatz

Understand

We evaluate the large-$N$ behavior of the superconformal indices of toric quiver gauge theories, and use it to find the entropy functions of the dual electrically charged rotating $\mathrm{AdS}_5$ black holes.

• To this end, we employ the recently proposed Bethe Ansatz method, and find a certain set of solutions to the Bethe Ansatz Equations of toric theories.
• This, in turn, allows us to compute the large-$N$ behavior of the index for these theories, including the infinite families $Y^{pq}$, $X^{pq}$ and $L^{pqr}$ of quiver gauge theories.
• Our results are in perfect agreement with the predictions made recently using the Cardy-like limit of the superconformal index.