Bulk quantum corrections to entwinement

TL;DR

This paper calculates quantum $1/N$ corrections to entwinement, a generalized entanglement measure in AdS$_3$/CFT$_2$, using the FLM formula and monodromy methods, with implications for the entanglement-geometry relationship.

Contribution

It provides a formal method to compute $1/N$ corrections to entwinement via a fictitious covering space and explicitly calculates these corrections for thermal states and small winding numbers.

Findings

Derived $1/N$ corrections to entwinement for thermal states.

Applied monodromy method to compute corrections to conformal blocks.

Identified universal finite-temperature corrections for large winding numbers.

Abstract

We determine $1/N$ corrections to a notion of generalized entanglement entropy known as entwinement dual to the length of a winding geodesic in asymptotically AdS$_3$ geometries. We explain how $1/N$ corrections can be computed formally via the FLM formula by relating entwinement to an ordinary entanglement entropy in a fictitious covering space. Moreover, we explicitly compute $1/N$ corrections to entwinement for thermal states and small winding numbers using a monodromy method to determine the corrections to the dominant conformal block for the replica partition function. We also determine a set of universal corrections at finite temperature for large winding numbers. Finally, we discuss the implications of our results for the "entanglement builds geometry" proposal.