Two-particle spectrum of tensor multiplets coupled to $AdS_3\times S^3$ gravity

We study the spectrum of certain two-particle operators in the supergravity regime of the D1-D5 system, focussing on the four-point correlators of tensor multiplets on $AdS_3\times S^3$ at tree level. In Mellin space, these are nicely determined by a single amplitude, which makes manifest the large $p$ limit, the connection with the flat space S-matrix, and the six dimensional conformal symmetry. We compute the $(1,1)\times \overline{(1,1)}$ superconformal blocks for the two-dimensional $\mathcal{N}=(4,4)$ conformal theory at the boundary, and then we obtain a formula for the anomalous dimensions of the operators exchanged in the symmetric and anti-symmetric flavor channels. These anomalous dimensions solve an unmixing problem which is analogous to the one in $AdS_5\times S^5$, with interesting modifications. Along the way we show how the $(1,1)\times \overline{(1,1)}$ superconformal blocks relate to those in $\mathcal{N}=4$ SYM in four dimensions, and we provide new intuition on the known data for $AdS_5\times S^5$.