Poking Holes in AdS/CFT: Bulk Fields from Boundary States

TL;DR

This paper introduces a boundary state-based, intrinsic CFT method to define local bulk operators in AdS3/CFT2, linking boundary states to bulk fields without relying on semi-classical geometry.

Contribution

It provides a state-independent, non-perturbative definition of bulk fields in AdS/CFT using twisted Ishibashi boundary states, applicable at large central charge.

Findings

Bulk fields create cross caps in CFT space-time.

Matrix elements satisfy bulk wave equations in black hole backgrounds.

Definition does not depend on semi-classical bulk geometry.

Abstract

We propose an intrinsic CFT definition of local bulk operators in AdS3/CFT2 in terms of twisted Ishibashi boundary states. The bulk field Phi(X) creates a cross cap, a circular hole with opposite edge points identified, in the CFT space-time. The size of the hole is parameterized by the holographic radial coordinate y. Our definition is state-independent, non-perturbative, and does not presume or utilize a semi-classical bulk geometry. We argue that, at large central charge, the matrix element between highly excited states satisfies the bulk wave equation in the AdS black hole background.