Counting all dyons in N=4 string theory

Atish Dabholkar*, Joao Gomes, Sameer Murthy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


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 languageEnglish
Article number059
Number of pages28
JournalJournal of High Energy Physics
Issue number5
Publication statusPublished - May 2011


  • Black Holes in String Theory
  • D-branes


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