Lectures on Microstate Geometries

Abstract

These are notes for some introductory lectures about microstate geometries and their construction. The first lecture considers BPS black holes in four dimensions as a way to introduce what one should expect from the BPS equations. The second lecture discusses the "no solitons without topology" theorem. The subsequent lectures move on to the construction and properties of bubbled microstate geometries in five dimensions. Since these are graduate lectures, they involve a strongly computational narrative intended to build some proficiency and understanding of supersymmetric solitons in five-dimensions. The narrative also regularly "plays tourist" pointing to specific features that are more general or have broader impact. The last sections contain brief comments on the larger setting of microstate geometries and describe some of the more recent developments. These lectures were given as a mini-course at the IPhT, Saclay in May, 2019.

53 pages; 4 figures

References in corpus (30)

• All supersymmetric solutions of minimal supergravity in five dimensions
• The Geometry of D=11 Killing Spinors
• Supergravity Microstates for BPS Black Holes and Black Rings
• Exact solutions for supersymmetric stationary black hole composites
• Bubbling Supertubes and Foaming Black Holes
• General Concentric Black Rings
• Supersymmetric black rings and three-charge supertubes
• Non-supersymmetric smooth geometries and D1-D5-P bound states
• Smooth horizonless geometries deep inside the black-hole regime
• Global Structure of Five-dimensional BPS Fuzzballs
• Quantizing N=2 Multicenter Solutions
• Black hole bound states in AdS_3 x S^2
• Momentum Fractionation on Superstrata
• Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions
• A bound on the entropy of supergravity?
• Hyperkahler Metrics from Periodic Monopoles
• Black Hole Deconstruction
• Bubbles on Manifolds with a U(1) Isometry
• Entropy Enhancement and Black Hole Microstates
• Non-BPS multi-bubble microstate geometries
• Localised $\mathbf{Ad}{\mathbf{S}}_5\times {\mathbf{S}}^5$ Black Holes
• Bolting Multicenter Solutions
• Hair-brane Ideas on the Horizon
• Geodesics in supersymmetric microstate geometries
• Godel space from wrapped M2-branes
• The Structure of BPS Equations for Ambi-polar Microstate Geometries
• Unlocking the Axion-Dilaton in 5D Supergravity
• Supersymmetry and Wrapped Branes in Microstate Geometries
• Microstate solutions from black hole deconstruction
• Geroch Group Description of Bubbling Geometries

Cited by in corpus (5)

• The Regge limit of AdS${}_3$ holographic correlators
• Microstate Renormalization in Deformed D1-D5 SCFT
• Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT${}_2$
• Black Holes and the Swampland: the Deep Throat revelations
• Lower bound for angular momenta of microstate geometries in five dimensions