Attractors and the Holomorphic Anomaly

Abstract

Motivated by the recently proposed connection between N=2 BPS black holes and topological strings, I study the attractor equations and their interplay with the holomorphic anomaly equation. The topological string partition function is interpreted as a wave-function obtained by quantizing the real cohomology of the Calabi-Yau. In this interpretation the apparent background dependence due to the holomorphic anomaly is caused by the choice of complex polarization. The black hole attractor equations express the moduli in terms of the electric and magnetic charges, and lead to a real polarization in which the background dependence disappears. Our analysis results in a generalized formula for the relation between the microscopic density of black hole states and topological strings valid for all backgrounds.

21 pages

References in corpus (13)

• N=2 Extremal Black Holes
• Supersymmetry and Attractors
• Black Hole Attractors and the Topological String
• Macroscopic Entropy of $N=2$ Extremal Black Holes
• Exact Counting of Black Hole Microstates
• Quantum Background Independence In String Theory
• Arithmetic and Attractors
• How Does a Fundamental String Stretch its Horizon?
• Microscopic Entropy of N=2 Extremal Black Holes
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• On the partition sum of the NS five-brane
• Topological M-theory as Unification of Form Theories of Gravity
• Matrix models, 4D black holes and topological strings on non-compact Calabi-Yau manifolds

Cited by in corpus (36)

• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Microscopic Black Hole Entropy in Theories with Higher Derivatives
• New Connections Between 4D and 5D Black Holes
• Precision Counting of Small Black Holes
• Direct Integration of the Topological String
• Hartle-Hawking Wave-Function for Flux Compactifications
• Black hole partition functions and duality
• Baby Universes in String Theory
• Hypermultiplets and Topological Strings
• Counting Dyons in N=8 String Theory
• Quantum Attractor Flows
• BPS Black Hole Degeneracies and Minimal Automorphic Representations
• Topological wave functions and heat equations
• Non-supersymmetric Black Holes and Topological Strings
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Attractors and Black Rings
• Topological String Theory on Compact Calabi-Yau: Modularity and Boundary Conditions
• Subleading and non-holomorphic corrections to N=2 BPS black hole entropy
• Quantum Entanglement of Baby Universes
• Refined Black Hole Ensembles and Topological Strings
• Black-holes, topological strings and large N phase transitions
• The Topological G2 String
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• Black Holes and the Spectrum of Half-BPS States in N=4 Supersymmetric String Theory
• Partition function of non-supersymmetric black holes in the supergravity limit
• On the critical points of the entropic principle
• Quantum A-infinity Structures for Open-Closed Topological Strings
• Geometric Perspective of Entropy Function: Embedding, Spectrum and Convexity
• Introduction to black hole entropy and supersymmetry
• A Comment on Quantum Distribution Functions and the OSV Conjecture
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• From Special Geometry to Black Hole Partition Functions
• Partition function of dyonic black holes in N=4 string theory
• Resolving Gravitational Singularities
• Topics in Open Topological Strings
• Geometric Transition as a Change of Polarization