An exact operator that knows its location

Abstract

We use conformal symmetry to define an AdS3 proto-field ϕ as an exact linear combination of Virasoro descendants of a CFT2 primary operator O. We find that both symmetry considerations and a gravitational Wilson line formalism lead to the same results. The operator ϕ has many desirable properties; in particular it has correlators that agree with gravitational perturbation theory when expanded at large c, and that automatically take the correct form in all vacuum AdS3 geometries, including BTZ black hole backgrounds. In the future it should be possible to use ϕ to probe bulk locality and black hole horizons at a non-perturbative level.