Two particle spectrum of tensor multiplets coupled to AdS3×S3 gravity

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We study certain infinite families of two-particle operators exchanged in 4pt correlators $⟨{\mathcal{O}}_{{p}_{1}}{\mathcal{O}}_{{p}_{2}}{\mathcal{O}}_{{p}_{3}}{\mathcal{O}}_{{p}_{4}}⟩$ of tensor multiplets living on the ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}$ background. This is the weakly curved, weakly coupled SUGRA theory dual to the D1-D5 system with RR flux. At tree level in Mellin space, all these correlators are nicely determined by a single amplitude, which makes manifest the large $p$ limit, the connection with the flat space S-matrix, and a six dimensional conformal symmetry. We compute the $(1,1)\ifmmode\times\else\texttimes\fi{}\overline{(1,1)}$ 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 two-particle operators exchanged in the symmetric and antisymmetric flavor channels. These anomalous dimensions solve a mixing problem which is analogous to the one in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ with interesting modifications. Along the way we show how the $(1,1)\ifmmode\times\else\texttimes\fi{}\overline{(1,1)}$ superconformal blocks relate to those in $\mathcal{N}=4$ SYM in four dimensions, and provide new intuition on the known data for ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$.