Exact Holographic Kinematics in AdS/CFT

TL;DR

This paper introduces an exact kinematic sector in holography within AdS/CFT, revealing a scale-manifesting Weyl frame that allows for precise bulk-boundary pairs without traditional approximations.

Contribution

It identifies a novel, exact kinematic sector in holography using a Weyl frame, distinct from the usual dynamical bulk geometry, and demonstrates its application to entanglement entropy.

Findings

Bulk-boundary pairs are exact and finite without approximations.

Weyl-frame two-point functions define entanglement entropy without replicas.

AdS geometry is a kinematic, not necessarily dynamical, structure.

Abstract

We propose that holography contains an exact kinematic sector distinct from holographic dynamics. The appropriate setting for this sector is a CFT on an open solid torus in the Weyl frame. The open solid torus introduces an intrinsic scale, and the Weyl frame makes this scale manifest as an extra bulk direction. The resulting bulk-boundary pairs are exact and finite: no cutoff, large-$N$ limit, strong-coupling assumption, or heavy-operator approximation is required. The AdS geometry appearing in this sector should be understood as a kinematic geometry; only in special CFTs and appropriate limits is it promoted to a dynamical semiclassical bulk. The standard boundary-anchored dictionary entries are recovered only as singular limits. As a striking demonstration, we show that Weyl-frame two-point functions provide a replica-free definition of entanglement entropy.