Abstract
The D1-D5 system has an orbifold point in its moduli space, at which it may be described by an mathcal{N} = (4,4) supersymmetric sigma model with target space MN/S(N) where M is {mathbb{T}}^4 or K3. In this paper we consider correlation functions involving chiral operators constructed from twist fields: we find explicit expressions for processes involving a twist n operator joining n twist operators of arbitrary twist. These expressions are universal, in that they are independent of the choice of M , and the final results can be expressed in a compact form. We explain how these results are relevant to the black hole microstate programme: one point functions of chiral operators can be used to reconstruct AdS3 near horizon regions of D1-D5 microstates and to match microstates constructed in supergravity with the CFT.
Highlights
Finds that associated with the black hole there are solutions that look like the black hole up to the horizon scale, but differ from it in the interior: the interior regions are replaced by these asymptotically AdS3 geometries
These expressions are universal, in that they are independent of the choice of M, and the final results can be expressed in a compact form. We explain how these results are relevant to the black hole microstate programme: one point functions of chiral operators can be used to reconstruct AdS3 near horizon regions of D1-D5 microstates and to match microstates constructed in supergravity with the CFT
While the black hole microstate programme was the main motivation for the current work, correlation functions in the orbifold SCFT are interesting in a number of other contexts
Summary
We review essential features of the D1-D5 orbifold CFT; a more complete review of the D1-D5 system can be found in [70]. The NS sector chiral primaries can be labeled as Om(p,q) where m is the twist and (p, q) labels the associated cohomology class. Each of the NS sector chiral primaries is mapped by spectral flow to a Ramond ground state operator (Om(pll,ql))nl → (OmR(lpl,ql))nl l l. The famous 3-charge black holes with macroscopic horizons discussed in [1] correspond to exciting the left moving sector with momentum P ; the resulting entropy is . As discussed in early works such as [73], most of the 3-charge microstates are associated with excitations over maximal and near maximal twist ground states (“long strings”) as there are more ways to fractionate the momentum over such states
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