Abstract
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 AdS5 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 Ypq , Xpq and Lpqr of quiver gauge theories. Our results are in perfect agreement with the predictions made recently using the Cardy-like limit of the superconformal index. We also explore the index structure in the space of chemical potentials and describe the pattern of Stokes lines arising in the conifold theory case.
Highlights
The Bekenstein-Hawking entropy of static dyonic BPS black holes in AdS4 was matched with the twisted index [2,3,4] of the dual ABJM theory on S2×S1 with a topological twist on S2 [5, 6]
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 AdS5 black holes
We show that the basic solutions to the Bethe Ansatz Equations (BAEs) for N = 4 Super Yang-Mills (SYM) used in [45] solve the BAEs for all toric quiver theories
Summary
We will be considering some generalities of index computations that we will later use in order to obtain large-N limits for the indices of toric theories. The integral representation of the superconformal index is given by [29, 49]. In order to estimate it, we will employ the technique of Bethe Ansatz Equations (BAE) [46, 47], which was recently used to find the large N behavior of the superconformal index of N = 4 SYM [45]. We can recast the integral representation (2.1) of the index as the sum over poles located at the solutions to certain transcendental equations called BAEs. Notice that as was shown in [46], the set of τ and σ satisfying (2.5) is dense in the domain {|p| < 1, |q| < 1} so the method is, in principle, applicable for any fugacities p and q. All the corresponding expressions can be found in [46]
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