Building a Gauge-Invariant Holographic Dictionary

Abstract

What natural CFT quantities can “see” in the interior of the bulk AdS in a diffeomorphism invariant way? And how can we use them to learn about the emergence of local bulk physics? Inspired by the Ryu-Takayanagi relation, we construct a class of simple non-local operators on both sides of the duality and demonstrate their equivalence. Integrals of free bulk fields along geodesics/minimal surfaces are dual to what we will call “OPE blocks”: Individual conformal family contributions to the OPE of local operators. Our findings can be utilized to reconstruct local bulk operators and unify a number of previously disconnected AdS/CFT results. We extend this kinematic correspondence to incorporate gravitational interactions in AdS3 by relating geodesic operators to the Virasoro OPE blocks, hence providing a natural CFT prescription for “gravitational dressing”. We conclude with discussion of preliminary results on an interesting CFT structure that generalizes our dictionary to include arbitrary local bulk interactions.