Counting all dyons in N =4 string theory

TL;DR

This paper develops a comprehensive microscopic framework to count all dyons in N=4 heterotic string theory, extending previous results to all charge invariants and confirming consistency with black hole and field theory degeneracies.

Contribution

It introduces a generalized method for computing dyon spectra for all invariants I, unifying previous special cases and deriving related superconformal field theories.

Findings

Degeneracy formula matches black hole entropy at large charges.

Results are consistent with field theory dyon counts at small charges.

The approach respects duality invariance and integrality of spectra.

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 = g.c.d.(Q \wedge 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.