Beyond Free Fields in AdS_3/CFT_2: Integrability in the Symmetric Product Orbifold

Building on earlier work with Eberhardt and Gaberdiel, where we identified the dual to the free symmetric orbifold CFT as string theory on AdS_3xS_3xT^4 with one unit of NS-NS flux, we consider the deformation away from this tensionless limit. This involves turning on a marginal deformation in the 2-cycle twisted sector in the CFT. We find that for large (BMN-like) operators, we can identify magnon excited states about the ground state which are governed by a hidden integrability. In particular, we argue for a dispersion relation for multi-magnon states exactly to all orders in the deformation parameter using an off-shell enhanced supersymmetry like in N=4 Super Yang-Mills. We find this dispersion to be consistent with the bulk dual having a non-zero RR three form flux turned on. We also show that the interactions of magnons are captured by a two body S-matrix which satisfies the Yang-Baxter equation. This clarifies the integrable structure of the perturbed symmetric orbifold CFT. It also indicates a way to incorporate RR flux in the dual worldsheet theory given the direct dictionary between the spacetime CFT and worldsheet CFT.