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

Abstract

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.

arXiv comment5 pages, 3 figures. Version 2: definition of the bulk operators is modified via the inclusion of an alternating sign: it creates a cross-cap instead of a hole with reflecting boundary. Other main conclusions are unaltered

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