Holography has an exact kinematic core: CFTs on an open solid torus give finite bulk relations without cutoffs
This paper argues that part of the AdS/CFT correspondence is purely kinematic and can be made exact. The authors show that placing a conformal field theory (CFT) on an open solid torus and working in a so-called Weyl frame (a rescaling of the metric that makes an intrinsic length scale manifest) produces finite, exact bulk–boundary relations. These relations do not need the usual shortcuts used in holography, such as imposing a short-distance cutoff, taking a large-N limit, assuming strong coupling, or focusing only on very heavy operators.
Concretely, the authors work in Euclidean signature on the geometry S1 × BD−1, an open solid torus built from a circle times a D−1 dimensional open ball. The torus introduces two radii that set a scale, and the Weyl frame promotes that boundary scale into an extra bulk direction. In this setting they derive two exact pairs. One pair equates the entanglement entropy between disjoint complementary regions in the CFT with an entanglement-wedge cross section (EWCS) in the bulk — a type of minimal surface that captures correlations between the regions. The other pair relates a Weyl-frame two-point function of a primary operator directly to the length of a finite geodesic lying entirely in the bulk. These relations are exact and finite for the spherical configurations they study.
The paper also gives an explicit chain that maps a simple boundary correlator to entanglement entropy without using the replica trick. The Weyl-frame two-point function is inverted to give the bulk geodesic length. Derivatives of that length fix a local bulk metric. From the metric one computes the EWCS volume, and that volume is then related — with a theory-dependent normalization called Evac — to the CFT entanglement entropy. Each step in this chain is finite and exact in the torus/Weyl-frame setup. As a consistency check, taking the singular boundary limit recovers standard results: in two dimensions the adjacent-region limit reproduces the familiar (c/3) log(|x−y|/ε) form, while in higher dimensions it reproduces the area law.