Comments on the Spectrum of CHL Dyons

Abstract

We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with $N=4$ supersymmetry. The partition function for these dyons is given in terms of Siegel modular forms associated with genus-two Riemann surfaces. We point out a subtlety in demonstrating S-duality invariance of the resulting degeneracies and give a prescription that makes the invariance manifest. We show, using M-theory lift of string webs, that the genus-two contribution captures the degeneracy only if a specific irreducibility criterion is satisfied by the charges. Otherwise, in general there can be additional contributions from higher genus Riemann surfaces. We analyze the negative discriminant states predicted by the formula. We show that even though there are no big black holes in supergravity corresponding to these states, there are multi-centered particle-like configurations with subleading entropy in agreement with the microscopic prediction and our prescription for S-duality invariance. The existence of the states is moduli dependent and we exhibit the curves of marginal stability and comment on its relation to S-duality invariance.

arXiv comment23 pages, 3 figures

References in corpus (26)

• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• Supergravity flows and D-brane stability
• EXTREMAL BLACK HOLES AND ELEMENTARY STRING STATES
• Counting Dyons in N=4 String Theory
• Exact Counting of Black Hole Microstates
• Exact solutions for supersymmetric stationary black hole composites
• New Connections Between 4D and 5D Black Holes
• Lectures on Superstring and M Theory Dualities
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• String Network
• A Stringy Cloak for a Classical Singularity
• BPS Nature of 3-String Junctions
• Asymptotic degeneracy of dyonic N=4 string states and black hole entropy
• Three-Pronged Strings and 1/4 BPS States in N=4 Super-Yang-Mills Theory
• Black hole partition functions and duality
• Dyon Spectrum in CHL Models
• Product Representation of Dyon Partition Function in CHL Models
• String Webs and 1/4 BPS Monopoles
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• Exact Black Hole Degeneracies and the Topological String
• Spectrum of CHL Dyons from Genus-Two Partition Function
• Re-Recounting Dyons in N=4 String Theory
• Planes, branes and automorphisms: II. Branes in motion
• String Webs and the Decay of Supersymmetric Particles
• String networks and supersheets

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