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AdS3/CFT2 holographic duality with N = (3,3) supersymmetry

We consider string theory on AdS3 x (S3 x S3 x S1) / Z2. This background supports N = 3 or 1 supersymmetry depending on the action of the Z2 orbifold. We consider the construction which has N = (3,3) supersymmetry and propose an AdS3/CFT2 holographic duality which states that string theory on this background is dual to the symmetric product orbifold of S0 / Z2, where S0 is a theory of four free fermions and one free boson. We show that the BPS spectra and the elliptic genera of the two sides of the duality match precisely, providing non-trivial support for our proposal. We also comment on the construction with N = 1 supersymmetry.