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We propose an intrinsic CFT definition of local bulk operators in AdS3/CFT2 in terms of twisted Ishibashi boundary states. The bulk field Phi(X) creates a cross cap, a circular hole with opposite edge points identified, in the CFT space-time. The size of the hole is parameterized by the holographic radial coordinate y. Our definition is state-independent, non-perturbative, and does not presume or utilize a semi-classical bulk geometry. We argue that, at large central charge, the matrix element between highly excited states satisfies the bulk wave equation in the AdS black hole background.
Herman Verlinde (Tue,) studied this question.