Abstract
Although BMPV black holes in flat space and in Taub-NUT space have identical near-horizon geometries, they have different indices from the microscopic analysis. For K3 compactification of type IIB theory, Sen et al. in a series of papers identified that the key to resolving this puzzle is the black hole hair modes: smooth, normalisable, bosonic and fermionic degrees of freedom living outside the horizon. In this paper, we extend their study to N = 4 CHL orbifold models. For these models, the puzzle is more challenging due to the presence of the twisted sectors. We identify hair modes in the untwisted as well as twisted sectors. We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree. Special care is taken to present details on the smoothness analysis of hair modes for rotating black holes, thereby filling an essential gap in the literature.
Highlights
Charge limit string theory gives a perfect match with the Bekenstein-Hawking entropy of the corresponding black hole in the two-derivative theory
We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree
We identify hair modes in the untwisted as well as twisted sectors and show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions perfectly match
Summary
We present relevant details on (2,0) supergravity coupled to nt number of tensor multiplets. If we consider pure (2, 0) theory coupled to nt tensor multiplets, we have the field content: a graviton, 4 left chiral gravitinos, 5 self-dual two-forms, nt anti-selfdual two-forms, 4nt fermions, and 5nt scalars. For the backgrounds we will work with, the scalars are set to constant values and the spin-1/2 fermions χαr are all set to zero With these conditions, the fermion sector field equations of motion simplify to ΓMNP DN ΨαP − HkMNP ΓN ΓkαβΨβP = 0, HsMNP ΓMN ΨαP = 0,. To discuss supersymmetry of black holes with hair, we will need the Killing spinor equations when the gravitino fields and the anti-self-dual fields are not set to zero.
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