An exact operator that knows its location

We use conformal symmetry to define an AdS(3) proto-field phi 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 phi 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 AdS(3) geometries, including BTZ black hole backgrounds. In the future it should be possible to use phi to probe bulk locality and black hole horizons at a non-perturbative level.