BLACK HOLE MICROSTATES AND HOLOGRAPHY IN THE D1D5 CFT
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In this thesis we exploit the setup of AdS3/CFT2 holography, and in particular the D1D5 two-dimensional CFT, to describe states dual to geometries relevant for the \fuzzball" proposal for the description of six-dimensional black hole microstates. Precise holographic dualities between CFT and bulk geometric objects are established and checked, both for 2 and 3-charge states. In particular, VEVs of CFT operators of small conformal dimension are checked to encode deviations from AdS3 geometry near the spacetime boundary. 4-point functions of the \heavy-heavy-light-light" type are also considered and matching is found between CFT and bulk computations via the usual AdS/CFT prescription, with the heavy states being dual to (simple) microstate geometries. In this context, the issue of the presence of spurious singularities at leading order in the large N limit is assessed and cancellations are found even without considering sub-leading corrections, at the cost of considering the full detail of the D1D5 CFT (i.e. including the Virasoro blocks of operators of small dimension charged under the internal SU(2)L SU(2)R R-symmetry group). Finally, more complicated 4-point functions, involving operators in the twisted sector of the CFT, are computed and the results are checked against known results in the literature with the aim of verifying the robustness of the (new) techniques used. Supersymmetric Ward identities are also derived, and checked for some cases, between correlators written in terms of bosons and in terms of fermions.
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