Dyon Spectrum in N=4 Supersymmetric Type II String Theories

TL;DR

This paper calculates the spectrum of quarter BPS dyons in certain orbifold compactifications of type II string theory, showing agreement between microscopic degeneracy and black hole entropy including curvature corrections.

Contribution

It provides the first detailed computation of dyon spectra in Z_2 and Z_3 orbifolds, demonstrating the match with black hole entropy beyond leading order.

Findings

Degeneracy formula matches black hole entropy with curvature corrections

Spectrum computed for Z_2 and Z_3 orbifolds of type II string theory

Small black hole entropy fails without curvature corrections

Abstract

We compute the spectrum of quarter BPS dyons in freely acting Z_2 and Z_3 orbifolds of type II string theory compactified on a six dimensional torus. For large charges the result for statistical entropy computed from the degeneracy formula agrees with the corresponding black hole entropy to first non-leading order after taking into account corrections due to the curvature squared terms in the effective action. The result is significant since in these theories the entropy of a small black hole, computed using the curvature squared corrections to the effective action, fails to reproduce the statistical entropy associated with elementary string states.