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 AdS3 × S3/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 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.

Highlights

  • We study the central charges and levels of 2d 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

  • In this paper we are interested in compactifications of type IIB string theory on K3 and the black strings emerging in this theory

  • We studied the central charges and levels of 2d N = (0, 4) superconformal field theories (SCFTs) dual to black strings that arise from D3-branes in type IIB compactifications on K3

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Summary

Macroscopics of 6d strings

It is known that black holes can have degrees of freedom living outside the horizon, known as hair, which contribute to the microscopic degeneracy [32, 33] It was shown in [15] that by performing the reduction at asymptotic infinity one includes the contributions of the hair. For the setups considered here, the classical contributions are the same whether they are computed in the near horizon geometry or at asymptotic infinity, the quantum corrections, on the other hand do depend on this. For this reason we shall perform computations at asymptotic infinity, reducing the action using the asymptotic solution. We conclude the section with a summary of the results obtained therein in anticipation of comparing with the microscopic computations in the subsequent section

Six-dimensional supergravity from type IIB on K3
Black string solutions
Classical contribution for ALE and ALF transverse spaces
Quantum contributions for ALF transverse spaces
Kaluza-Klein spectrum
Contribution of massive KK modes to one-loop Chern-Simons terms
Summary
Microscopics of 6d strings
Transverse ALE spaces
Transverse ALF spaces
Conclusion and outlook
B Summation of 3d one-loop corrections
Relevant spectrum
Correction to the left level
Correction to the right level

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