Bulk quantum corrections to entwinement

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.