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Deforming Symmetric Product Orbifolds: A tale of moduli and higher spin currents

We analyze how deforming symmetric product orbifolds of two-dimensional $\mathcal{N}=2$ conformal field theories by an exactly marginal operator lifts higher spin currents present at the orbifold point. We find on the one hand that these currents are universally lifted regardless of the underlying CFT. On the other hand the details of the lifting are surprisingly non-universal, with dependence on the central charge of the underlying CFT and the specific marginal operator in use. In the context of the AdS/CFT correspondence, our results illustrate the mechanism by which the stringy spectrum turns into a supergravity spectrum when moving through the moduli space. They also provide further evidence that symmetric product orbifolds of $\mathcal{N}=2$ minimal models are holographic.