Mixed Rademacher and BPS Black Holes

Abstract

Dyonic 1/4-BPS states in Type IIB string theory compactified on $\mathrm{K}3\times T^2$ are counted by meromorphic Jacobi forms. The finite parts of these functions, which are mixed mock Jacobi forms, account for the degeneracy of states stable throughout the moduli space of the compactification. In this paper, we obtain an exact asymptotic expansion for their Fourier coefficients, refining the Hardy-Ramanujan-Littlewood circle method to deal with their mixed-mock character. The result is compared to a low-energy supergravity computation of the exact entropy of extremal dyonic 1/4-BPS single-centered black holes, obtained by applying supersymmetric localization techniques to the quantum entropy function.

42 pages

References in corpus (11)

• Mock Theta Functions
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• A Farey Tail for Attractor Black Holes
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Nonperturbative black hole entropy and Kloosterman sums
• Comments on the Spectrum of CHL Dyons
• Product Representation of Dyon Partition Function in CHL Models
• A Farey tale for N=4 dyons
• Re-Recounting Dyons in N=4 String Theory
• Asymptotic Expansion of the N=4 Dyon Degeneracy

Cited by in corpus (12)

• Free partition functions and an averaged holographic duality
• Vafa-Witten invariants from modular anomaly
• Dyonic black hole degeneracies in $\mathcal{N}=4$ string theory from Dabholkar-Harvey degeneracies
• The gravitational path integral for $N=4$ BPS black holes from black hole microstate counting
• Mock modularity from black hole scattering states
• Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle
• Arithmetic of decay walls through continued fractions: a new exact dyon counting solution in $\mathcal{N}=4$ CHL models
• Rademacher expansion of a Siegel modular form for $\mathcal{N}=4$ counting
• Quantum Modular $\hat{Z}{}^G$-Invariants
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• On the exact entropy of $\mathcal{N}=2$ black holes