A Twist in the Dyon Partition Function
arXiv:0911.1563 · doi:10.1007/JHEP05(2010)028
Abstract
In four dimensional string theories with N=4 and N=8 supersymmetries one can often define twisted index in a subspace of the moduli space which captures additional information on the partition function than the ones contained in the usual helicity trace index. We compute several such indices in type IIB string theory on K3 x T^2 and T^6, and find that they share many properties with the usual helicity trace index that captures the spectrum of quarter BPS states in N=4 supersymmetric string theories. In particular the partition function is a modular form of a subgroup of Sp(2,Z) and the jumps across the walls of marginal stability are controlled by the residues at the poles of the partition function. However for large charges the logarithm of this index grows as 1/n times the entropy of a black hole carrying the same charges where n is the order of the symmetry generator that is used to define the twisted index. We provide a macroscopic explanation of this phenomenon using quantum entropy function formalism. The leading saddle point corresponding to the attractor geometry fails to contribute to the twisted index, but a Z_n orbifold of the attractor geometry produces the desired contribution.
LaTeX file, 35 pages; v2: references added
References in corpus (27)
- Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
- CHL Dyons and Statistical Entropy Function from D1-D5 System
- Magnetic Monopole Dynamics, Supersymmetry, and Duality
- Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
- Comments on the Spectrum of CHL Dyons
- Arithmetic of Quantum Entropy Function
- Holographic Description of AdS_2 Black Holes
- Product Representation of Dyon Partition Function in CHL Models
- A Farey tale for N=4 dyons
- Dyon Spectrum in N=4 Supersymmetric Type II String Theories
- Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
- Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
- Two Centered Black Holes and N=4 Dyon Spectrum
- N=8 Dyon Partition Function and Walls of Marginal Stability
- Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
- Supersymmetry, Localization and Quantum Entropy Function
- Asymptotic Expansion of the N=4 Dyon Degeneracy
- Generalities of Quarter BPS Dyon Partition Function and Dyons of Torsion Two
- Wall Crossing Formula for N=4 Dyons: A Macroscopic Derivation
- Arithmetic of N=8 Black Holes
- U-duality Invariant Dyon Spectrum in type II on T^6
- Adding Charges to N=4 Dyons
- Generalized Kac-Moody Algebras from CHL dyons
- The mixed black hole partition function for the STU model
- On the dyon partition function in N=2 theories
- Genus Two Surface and Quarter BPS Dyons: The Contour Prescription
- Perturbative tests of non-perturbative counting
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- Microscopic and Macroscopic Entropy of Extremal Black Holes in String Theory
- Black Hole Microstate Counting and its Macroscopic Counterpart
- Discrete Information from CHL Black Holes
- BKM Lie superalgebras from counting twisted CHL dyons
- How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
- A universal formula for the density of states in theories with finite-group symmetry
- Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
- BKM Lie superalgebras from counting twisted CHL dyons -- II
- Negative discriminant states in N=4 supersymmetric string theories
- Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
- Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy
- Supersymmetrization of deformed BMS algebras
- Dualities in CHL-Models
- BPS Spectrum, Indices and Wall Crossing in N=4 Supersymmetric Yang-Mills Theories
- BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications
- BKM Lie superalgebra for the Z_5 orbifolded CHL string
- Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
- Mock Modularity In CHL Models
- Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the Model