Recounting Dyons in N=4 String Theory

TL;DR

This paper derives the degeneracies of 4D BPS black holes in N=4 string theory from 5D degeneracies using a relation between black holes in different dimensions, confirming a prior conjecture.

Contribution

It establishes a precise mathematical connection between 4D and 5D black hole degeneracies via automorphic forms, confirming a longstanding conjecture.

Findings

Degeneracies given by Fourier coefficients of a weight 10 automorphic form

Exact agreement with the conjecture by Dijkgraaf, Verlinde and Verlinde

Provides a new method to compute 4D black hole degeneracies

Abstract

A recently discovered relation between 4D and 5D black holes is used to derive weighted BPS black hole degeneracies for 4D N=4 string theory from the well-known 5D degeneracies. They are found to be given by the Fourier coefficients of the unique weight 10 automorphic form of the modular group Sp(2,Z). This result agrees exactly with a conjecture made some years ago by Dijkgraaf, Verlinde and Verlinde.