A Note on D1-D5 Entropy and Geometric Quantization

TL;DR

This paper quantizes the space of 2-charge fuzzballs in IIB supergravity on K3, achieving an entropy calculation that exactly matches the D1-D5 black hole entropy, thus providing a precise microscopic understanding.

Contribution

It generalizes Rychkov's approach to the full moduli space of K3 fuzzballs, filling a gap in the literature with a simple observation.

Findings

Exact match between fuzzball entropy and D1-D5 black hole entropy

Generalization of previous partial results to full K3 moduli space

Provides a microscopic quantization of 2-charge fuzzballs

Abstract

We quantize the space of 2-charge fuzzballs in IIB supergravity on $K3$. The resulting entropy precisely matches the D1-D5 black hole entropy, including a specific numerical coefficient. A partial match (ie., a smaller coefficient) was found by Rychkov a decade ago using the Lunin-Mathur subclass of solutions - we use a simple observation to generalize his approach to the full moduli space of $K3$ fuzzballs, filling a small gap in the literature.