An Exact Operator That Knows Its Location

TL;DR

This paper constructs an exact AdS$_3$ proto-field operator using conformal symmetry and Virasoro descendants, which reproduces gravitational correlators and adapts to various AdS$_3$ geometries, including black holes.

Contribution

It introduces a new exact operator in AdS$_3$/CFT$_2$ that captures bulk physics non-perturbatively using Virasoro symmetry and Wilson lines.

Findings

Operator matches gravitational perturbation theory at large central charge

Automatically adapts to all vacuum AdS$_3$ geometries

Potential to probe bulk locality and horizons non-perturbatively

Abstract

We use conformal symmetry to define an AdS$_3$ proto-field $\phi$ 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 $\phi$ 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.