A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled

TL;DR

This paper develops a kernel to compute off-diagonal three-point coefficients in AdS3/CFT2, enabling the probing of the geometry behind black hole horizons regardless of entanglement, revealing how horizon geometry gets disentangled.

Contribution

It introduces a new kernel for the Wightman function that is independent of entanglement, allowing exploration of emergent geometries without thermal entanglement.

Findings

Kernel equals average off-diagonal matrix element squared of a primary operator

Allows computation of Wightman function for arbitrary entanglement

Probes geometry behind the horizon beyond thermally entangled states

Abstract

In the AdS/CFT correspondence eternal black holes can be viewed as a specific entanglement between two copies of the CFT: the thermofield double. The statistical CFT Wightman function can be computed from a geodesic between the two boundaries of the Kruskal extended black hole and therefore probes the geometry behind the horizon. We construct a kernel for the AdS3/CFT2 Wightman function that is independent of the entanglement. This kernel equals the average off-diagonal matrix element squared of a primary operator. This allows us to compute the Wightman function for an arbitrary entanglement between the double copies and probe the emergent geometry between a left- and right-CFT that are not thermally entangled.