Two Centered Black Holes and N=4 Dyon Spectrum

TL;DR

This work links the discontinuous wall-crossing of N=4 dyon degeneracies to the entropy of two-centered small black holes, showing that the jump across marginal stability walls can be precisely accounted for by a multicenter black hole configuration. By analyzing the exact dyon spectrum and performing a detailed supergravity construction with a two-centered setup, the authors demonstrate that the jump equals the sum of the entropies of a small electric and a small magnetic black hole, confirming a deeper microscopic–macroscopic correspondence beyond leading-order black hole entropy. The findings indicate that multicentered black holes encode not only the existence of certain dyon states but also the specific, exponentially suppressed changes in degeneracy across walls. This strengthens the bridge between exact stringy dyon spectra and the geometry of multicenter black hole solutions.

Abstract

The exact spectrum of dyons in a class of N=4 supersymmetric string theories is known to change discontinuously across walls of marginal stability. We show that the change in the degeneracy across the walls of marginal stability can be accounted for precisely by the entropy of two centered small black holes which disappear as we cross the walls of marginal stability.