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In this work, we calculate correlators of long strings onAdS$_3\times$S$^3\times$T$^4$ with pure NS-NS flux. We first construct physicalvertex operators that correspond to long strings. Due to the GSO projection,they depend on the parity of the spectral flow parameter $w$. For a given $w$,we construct the physical operators that have the lowest space-time weights inboth the NS and R sector. Then, we calculate three point correlators for eachpossible type of parities of spectral flows. We find that the recursionrelations of correlators in the bosonic SL$(2,\mathbb{R})$ WZW model can beunderstood from the equivalence of these superstring correlators with differentpicture choices. Furthermore, after carefully mapping the vertex operators toappropriate operators in the dual CFT, we find that once the fermioniccontributions together with the picture changing effects are correctly takeninto account, some mathematical identities of covering maps lead to thematching of the correlators of the two sides. We check this explicitly at theleading order in the conformal perturbation computation and conjecture thatthis remains correct to all orders.

Correlators of long strings on AdS$_3\times$S$^3\times$T$^4$