Black hole entropy function for toric theories via Bethe Ansatz

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 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. 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.

Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization

“…Going beyond the Cardy-like limit, however, seems more formidable. The absence of a Bethe Ansatz description for the superconformal index seems to block a route that was successfully taken in the 4d context [42,43]. It would be interesting to consider near-BPS configurations by turning on temperature or slightly violating the BPS constraint (4.54), in the same spirit as [50].…”

“…Several groups have now independently reproduced the entropy function by studying the partition function or the superconformal index of N " 4 SYM [34][35][36] by slightly reinterpreting the original work in the superconformal index [26]. Further extensions for the general growth of the N " 1 superconformal index [37][38][39][40][41] including via the Bethe-Ansatz approach [42,43] have been achieved. After this important progress, the generalizations to other dimensions were also considered.…”

AdS black holes, holography and localization

“…Using SLð2; ZÞ, the authors of Hong and Liu (2018) have found many other solutions of the Bethe equations for N ¼ 4 SYM at finite s. Non-standard solutions corresponding to continua of Bethe vacua have been found in Arabi . The solution (5.19) extends to more general quivers (Hosseini et al 2017c;González Lezcano and Pando Zayas 2020;Lanir et al 2020). 59 Notice that b is not really a temperature, but rather a parameterization of the modular parameter of the torus.…”

Supersymmetric phases of 4d $$ \mathcal{N} $$ = 4 SYM at large N

“…Following the insightful observation of [3], this puzzle has been revisited recently [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] The emergent picture shows that there is actually an exponential growth of states contained in the index, which is captured by the saddle-point estimate if one allows the potentials σ, τ , ϕ to take values in the complex plane away from the pure imaginary values assumed in [2]. 1 There are essentially three strands of analysis contained in the recent progress:…”

“…The 20 This region lies inside the region in red in the figure 4 to the right which means that there is a supersymmetric (but not necessarily extremal) black-hole-like solution that exists in supergravity). 21 A partial phase diagram for N = 4 SYM was first presented in [8]. It focused on the subset of (1, r) configurations, with r ∈ Z which is equivalent to our figure 7 after mapping conventions (see Footnote 32).…”