Asymptotic Expansion of the N=4 Dyon Degeneracy

TL;DR

This work analyzes power-suppressed and exponentially suppressed corrections to the quarter-BPS dyon degeneracy in N=4 string theories. It constructs and evaluates an organized asymptotic expansion of the statistical entropy via the statistical entropy function Γ_B, obtaining corrections up to 1/charge^2 and the first exponential term, and compares them to exact degeneracies to assess domain applicability. The authors connect these microscopic corrections to macroscopic physics through the quantum entropy function, highlighting multi-saddle contributions (including Z_N orbifolds) and proposing a universal structure for exponentially suppressed corrections across extremal black holes. The findings illuminate the interplay between microscopic exact formulas and macroscopic entropy calculations and point toward OSV-like relations governing subleading black hole entropy corrections.

Abstract

We study various aspects of power suppressed as well as exponentially suppressed corrections in the asymptotic expansion of the degeneracy of quarter BPS dyons in N=4 supersymmetric string theories. In particular we explicitly calculate the power suppressed corrections up to second order and the first exponentially suppressed corrections. We also propose a macroscopic origin of the exponentially suppressed corrections using the quantum entropy function formalism. This suggests a universal pattern of exponentially suppressed corrections to all four dimensional extremal black hole entropies in string theory.

Figures (2)

• Figure 1: 2-loop graphs using the vertices from $F_0$.
• Figure 2: 1-loop graph using a 2-vertex from $F_1$.