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We compute the worldsheet sphere partition function of string theory on global AdS ₃ 3 with pure NS-NS flux. Because of an unfixed Möbius symmetry on the worldsheet, there is a cancellation of infinities and only a part of the answer is unambiguous. We show that it precisely reproduces the holographic Weyl anomaly and the ambiguous terms correspond to the possible counterterms of the boundary CFT.
Eberhardt et al. (Wed,) studied this question.