### 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.

Original language | English (US) |
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Pages (from-to) | 543-561 |

Number of pages | 19 |

Journal | Nuclear Physics B |

Volume | 484 |

Issue number | 3 |

DOIs | |

State | Published - Jan 27 1997 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

Dijkgraaf, R., Verlinde, E., & Verlinde, H. (1997). Counting dyons in N = 4 string theory.

*Nuclear Physics B*,*484*(3), 543-561. https://doi.org/10.1016/S0550-3213(96)00640-2