# Black Holes and (0,4) SCFTs from Type IIB on K3

## TL;DR

This paper investigates the properties of 2d (0,4) superconformal field theories arising from D3-branes on K3 surfaces in type IIB string theory, matching microscopic and macroscopic entropy calculations for related black holes.

## Contribution

It provides a detailed computation of central charges and levels of 2d SCFTs from both microscopic string theory and supergravity, including quantum corrections, establishing their agreement.

## Key findings

- Microscopic and supergravity calculations of central charges agree.
- Quantum corrections are essential for matching results.
- The study enhances understanding of black hole microstates in string theory.

## Abstract

We study the central charges and levels of 2d $\mathcal{N}=(0,4)$ superconformal field theories that are dual to four- and five-dimensional BPS black holes in compactifications of type IIB string theory on a K3 surface. They arise from wrapping a D3-brane on a curve $C$ inside K3 and have transverse space either an ALE or ALF space. These D3-branes have an AdS$_3 \times \mathrm{S}^3/ \Gamma$ near horizon geometry where $\Gamma$ is a discrete subgroup of $SU(2)$. We compute the central charges and levels of the 2d SCFTs both in the microscopic picture and from six-dimensional $\mathcal{N}=(2,0)$ supergravity. These quantities determine the black hole entropy via Cardy's formula. We find agreement between the microscopic and macroscopic computations. The contributions from one-loop quantum corrections to the macroscopic result are crucial for this matching.