Black hole microstates and supersymmetric localization

Abstract

This thesis focuses mainly on understanding the origin of the Bekenstein-Hawking entropy for a class of four- and five-dimensional BPS black holes in string/M-theory. To this aim, important ingredients are holography and supersymmetric localization. Using the method of supersymmetric localization, the Euclidean path integrals for supersymmetric field theories on ${\Sigma }_{\mathfrak{g}}\times T^n$ $(n=1,2)$, with at least four real supercharges, can be reduced to a matrix integral that depends on background magnetic fluxes and chemical potentials for the global symmetries of the theory. This defines the topologically twisted index which, upon extremization with respect to the chemical potentials, is conjectured to reproduce the entropy of magnetically charged static BPS AdS${}_{4/5}$ black holes/strings. We solve a number of such matrix models both in three and four dimensions and provide general formulae in the large $N$ limit. We then use these results to provide the microscopic realization of the entropy of a class of BPS black holes in $\mathcal{N}=2$ gauged supergravity. Finally, inspired by our previous results, we put forward an extremization principle for reproducing the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS${}_5\times S^5$.

208 pages; PhD thesis; mostly based on arXiv:1604.03122, arXiv:1604.03397, arXiv:1611.09374, arXiv:1705.05383, arXiv:1707.06884 with some new results/observations; V2: few signs corrected, typos removed

References in corpus (31)

• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Supersymmetric multi-charge AdS_5 black holes
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Exact two-dimensional superconformal R-symmetry and c-extremization
• Witten Index and Wall Crossing
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• Localization on Hopf surfaces
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Brane Tilings and M2 Branes
• Supersymmetry enhancement by monopole operators
• M2-branes on Orbifolds of the Cone over Q^{1,1,1}
• Entropy function and attractors for AdS black holes
• New supersymmetric AdS4 type II vacua
• Comments on 1/16 BPS Quantum States and Classical Configurations
• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• Near-horizon geometries of supersymmetric AdS(5) black holes
• Static BPS Black Holes in AdS4 with General Dyonic Charges
• An Index Formula for Supersymmetric Quantum Mechanics
• BPS black holes in N=2 D=4 gauged supergravities
• Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes
• Comments on the Casimir energy in supersymmetric field theories
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• BPS black hole horizons from massive IIA
• Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories
• BPS black holes from massive IIA on S${}^6$
• AdS/CFT with Tri-Sasakian Manifolds
• Phases of planar 5-dimensional supersymmetric Chern-Simons theory
• Parameter spaces of massive IIA solutions
• Penrose limits and spin chains in the GJV/CS-SYM duality
• c-extremization from toric geometry

Cited by in corpus (6)

• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• On the quantum entropy function in 4d gauged supergravity
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• One-loop determinants for black holes in 4d gauged supergravity
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail