Comments on integrability in the symmetric orbifold

Abstract

We present a map between the excitation of the symmetric-product orbifold CFT of T4, and of the worldsheet-integrability description of AdS3 × S3 × T4 of Lloyd, Ohlsson Sax, Sfondrini, and Stefański at k = 1. We discuss the map in the absence of RR fluxes, when the theory is free, and at small RR flux, h ≪ 1, where the symmetric-orbifold CFT is deformed by a marginal operator from the twist-two sector. We discuss the recent results of Gaberdiel, Gopakumar, and Nairz, who computed from the perturbed symmetric-product orbifold the central extension to the symmetry algebra of the theory and its coproduct. We show that it coincides with the h ≪ 1 expansion of the lightcone symmetry algebra known from worldsheet integrability, and that hence the S matrix found by Gaberdiel, Gopakumar, and Nairz maps to the one bootstrapped by the worldsheet integrability approach.