Higgsing the stringy higher spin symmetry

It has recently been argued that the symmetric orbifold theory of T⁴ is dual to string theory on AdS₃×S³×T⁴ at the tensionless point. At this point in moduli space, the theory possesses a very large symmetry algebra that includes, in particular, a W_∞ algebra capturing the gauge fields of a dual higher spin theory. Using conformal perturbation theory, we study the behaviour of the symmetry generators of the symmetric orbifold theory under the deformation that corresponds to switching on the string tension. We show that the generators fall nicely into Regge trajectories, with the higher spin fields corresponding to the leading Regge trajectory. We also estimate the form of the Regge trajectories for large spin, and find evidence for the familiar logarithmic behaviour, thereby suggesting that the symmetric orbifold theory is dual to an AdS background with pure RR flux.