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We propose an intrinsic CFT definition of local bulk operators in AdS3/CFT2in terms of twisted Ishibashi boundary states. The bulk field Phi(X) creates across cap, a circular hole with opposite edge points identified, in the CFTspace-time. The size of the hole is parameterized by the holographic radialcoordinate y. Our definition is state-independent, non-perturbative, and doesnot presume or utilize a semi-classical bulk geometry. We argue that, at largecentral charge, the matrix element between highly excited states satisfies thebulk wave equation in the AdS black hole background.

Poking Holes in AdS/CFT: Bulk Fields from Boundary States