In this thesis we investigate on the microscopic nature of the entropy of black holes in string theory in the context of AdS/CFT correspondence. We focus our attention on two particularly interesting cases in different dimensions. First, we consider static dyonic BPS black holes in AdS$_4$ in 4d $mathcal{N}=2$ gauged supergravities with vector and hyper multiplets. More precisely, we focus on the example of BPS black holes in AdS$_4 imes S^6$ in massive Type IIA, whose dual threedimensional holographic description is known and simple. To provide a microscopic counting of the black hole entropy we employ a topologically twisted index in the dual field theory, which can be computed exactly and nonperturbatively with localization techniques. We find perfect match at leading order. Second, we turn to rotating electricallycharged BPS black holes in AdS$_5 imes S^5$ in Type IIB. Here, the microscopic entropy counting is done in terms of the superconformal index of the dual $cN=4$ SuperYangMills theory. We proceed by deriving a new formula, which expresses the index as a finite sum over the solution set of certain transcendental equations, that we dub Bethe Ansatz Equations, of a function evaluated at those solutions. Then, using the latter formula, we reconsider the large $N$ limit of the superconformal index. We find an exponentially large contribution which exactly reproduces the BekensteinHawking entropy of the black holes of GutowskiReall. Besides, the large $N$ limit exhibits a complicated structure, with many competing exponential contributions and Stokes lines, hinting at new physics.
A tale of two indices or how to count black hole microstates in AdS/CFT
Milan, Paolo
2019
Abstract
In this thesis we investigate on the microscopic nature of the entropy of black holes in string theory in the context of AdS/CFT correspondence. We focus our attention on two particularly interesting cases in different dimensions. First, we consider static dyonic BPS black holes in AdS$_4$ in 4d $mathcal{N}=2$ gauged supergravities with vector and hyper multiplets. More precisely, we focus on the example of BPS black holes in AdS$_4 imes S^6$ in massive Type IIA, whose dual threedimensional holographic description is known and simple. To provide a microscopic counting of the black hole entropy we employ a topologically twisted index in the dual field theory, which can be computed exactly and nonperturbatively with localization techniques. We find perfect match at leading order. Second, we turn to rotating electricallycharged BPS black holes in AdS$_5 imes S^5$ in Type IIB. Here, the microscopic entropy counting is done in terms of the superconformal index of the dual $cN=4$ SuperYangMills theory. We proceed by deriving a new formula, which expresses the index as a finite sum over the solution set of certain transcendental equations, that we dub Bethe Ansatz Equations, of a function evaluated at those solutions. Then, using the latter formula, we reconsider the large $N$ limit of the superconformal index. We find an exponentially large contribution which exactly reproduces the BekensteinHawking entropy of the black holes of GutowskiReall. Besides, the large $N$ limit exhibits a complicated structure, with many competing exponential contributions and Stokes lines, hinting at new physics.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.14242/67118
URN:NBN:IT:SISSA67118