## Abstract

For dyons in heterotic string theory compactified on a six-torus, with electric charge vector Q and magnetic charge vector P, the positive integer I equivalent to gcd(Q boolean AND P) is an invariant of the U-duality group. We propose the microscopic theory for computing the spectrum of all dyons for all values of I, generalizing earlier results that exist only for the simplest case of I = 1. Our derivation uses a combination of arguments from duality, 4d-5d lift, and a careful analysis of fermionic zero modes. The resulting degeneracy agrees with the black hole degeneracy for large charges and with the degeneracy of field-theory dyons for small charges. It naturally satisfies several physical requirements including integrality and duality invariance. As a byproduct, we also derive the microscopic (0, 4) superconformal field theory relevant for computing the spectrum of five-dimensional Strominger-Vafa black holes in ALE backgrounds and count the resulting degeneracies.

Original language | English |
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Article number | 059 |

Number of pages | 28 |

Journal | Journal of High Energy Physics |

Volume | 2011 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2011 |

## Keywords

- Black Holes in String Theory
- D-branes
- BPS STATES
- D-BRANES
- MONOPOLES
- INSTANTONS