Counting dyons in N = 4 string theory

1996/07/03 by Robbert Dijkgraaf, R. Dijkgraaf, Erik Verlinde +3 · 8 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Degeneracy (biology) #Duality (order theory) #Dyon #Homotopy and Cohomology in Algebraic Topology #String (physics) #String theory #Type (biology) #hep-th

paper · pdf · doi:10.1016/s0550-3213(96)00640-2

published as Nucl.Phys.B484:543-561,1997 · 22 pages, latex, one epsf-figure

arxiv created 1996/07/03 · openalex publication_date 1997/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We present a microscopic index formula for the degeneracy of dyons in four-dimensional N=4 string theory. This counting formula is manifestly symmetric under the duality group, and its asymptotic growth reproduces the macroscopic Bekenstein-Hawking entropy. We give a derivation of this result in terms of the type II five-brane compactified on K3, by assuming that its fluctuations are described by a closed string theory on its world-volume. We find that the degeneracies are given in terms of the denominator of a generalized super Kac-Moody algebra. We also discuss the correspondence of this result with the counting of D-brane states.

Citations

• Strong-weak coupling duality and non-perturbative effects in string theory
• Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole moduli space, and SL (2,Z) invariance in string theory
• Black holes and thermodynamics
• Algebras, BPS states, and strings
• Dirichlet Branes and Ramond-Ramond Charges
• Automorphic forms onO s +2,2(R) and infinite products
• STRONG–WEAK COUPLING DUALITY IN FOUR-DIMENSIONAL STRING THEORY
• Entropy of 4D extremal black holes
• Generalized second law of thermodynamics in black-hole physics
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Holes and Entropy

Cited by

• The elliptic genus of Calabi-Yau 3- and 4-folds, product formulae and generalized Kac-Moody algebras
• Black hole entropy function, attractors and precision counting of microstates
• Lost chapters in CHL black holes: untwisted quarter-BPS dyons in the ℤ2 model
• Quantum Corrections and Extremality: A Generalized Universal Relation
• Non-perturbative temperature instabilities in N = 4 strings
• A twist in the dyon partition function
• Quantum black hole entropy and the holomorphic prepotential of N=2 supergravity
• Black hole hair removal: non-linear analysis