Correlation functions in the D1-D5 orbifold CFT

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 $M^N\mathrm{/}S(N)$ 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 AdS${}_3$ near horizon regions of D1-D5 microstates and to match microstates constructed in supergravity with the CFT.