An Exact Operator That Knows Its Location

Abstract

We use conformal symmetry to define an AdS$_3$ proto-field $ϕ$ as an exact linear combination of Virasoro descendants of a CFT$_2$ primary operator $\mathcal{O}$. 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 AdS$_3$ 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.

24+33 pages, 2 figures; V2: refs added, terminology updated