Effective AdS3/CFT2

In [1], it was pointed out that superstring theory on AdS ₃ with (NS, NS) B-field background and R _AdS/l _s = $$ \sqrt{k} $$ k < 1 is dual to a symmetric product CFT deformed by an operator in the ℤ ₂ twisted sector. We generalize the analysis of [1] to k > 1, and show that the resulting picture matches that discussed in the bosonic case in [2]. We argue that in the critical case, k = 1 [3], the ℤ ₂ twisted deformation remains non-trivial. This resolves some confusions in the literature.