A Note on D1-D5 Entropy and Geometric Quantization

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.