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Lectures on AdS Black Holes, Holography and Localization

Alberto Zaffaroni

Abstract

In these lectures I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimensions equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS$_4$ black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS$_5$ black holes.

Lectures on AdS Black Holes, Holography and Localization

Abstract

In these lectures I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimensions equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS black holes.

Paper Structure

This paper contains 43 sections, 196 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Content of the lectures
  3. AdS black holes in $d\ge4$
  4. AdS black holes and holography
  5. Kerr--Newman black holes and generalizations
  6. Magnetically charged black holes with a twist
  7. Computing the entropy
  8. The grand canonical partition function
  9. The supersymmetric index
  10. Entropy functionals and the attractor mechanism
  11. $\mathcal{I}$-extremization
  12. The topologically twisted index
  13. The topological twist
  14. The localization formula
  15. The BPS locus
  16. ...and 28 more sections

Figures (1)

  • Figure 1: Plots of the density of eigenvalues $\rho(t)$ and the function $\delta v(t)$ for $N=75$, $\Delta_1=0.3$, $\Delta_2=0.4$, $\Delta_3=0.5$ with $\sum_a\Delta_a=2\pi$ and $k=1$. The blue dots represent the numerical simulation, while the solid grey line is the analytical result.