A bstract We study the central charges and levels of 2d N $$ mathcal{N} $$ = (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)× S_(3)/Γ near horizon geometry where Γ 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 N $$ mathcal{N} $$ = (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.
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