Quantum Entanglement of Circular Strings as a Probe for Topologically Charged Spacetimes

TL;DR

This paper develops a quantum probe method using circular strings to measure entanglement entropy, revealing geometric features of topologically charged spacetimes like monopoles and wormholes.

Contribution

It introduces a framework for quantizing string fluctuations in curved spacetimes to use entanglement as a probe of topology and geometry beyond classical observables.

Findings

Entanglement distinguishes between monopole and wormhole geometries.

Probe entanglement is highly sensitive to the spacetime's deficit angle.

Quantum correlations serve as diagnostic tools for spacetime topology.

Abstract

Motivated by the limited understanding of entanglement entropy in non-asymptotically AdS spacetimes, we develop a framework in which a circular string is embedded as a quantum probe in a spherically symmetric curved spacetime, and its quadratic fluctuations are quantized using the squeezed-state formalism. This construction naturally yields two mode quantum states and the associated von Neumann entropy, providing a direct measure of particle antiparticle entanglement. The resulting entanglement serves as an effective probe of the underlying geometry, granting access to intrinsic features that are not readily captured by classical observables such as geodesic motion. As a concrete application, and as representative toy models of spacetimes with topological defects, including wormhole geometries, we investigate backgrounds with topological charge, focusing on global monopole and monopole wormhole configurations. We show that the entanglement generated by the probe string exhibits a clear qualitative distinction between these backgrounds and is highly sensitive to the global structure of the spacetime, in particular to the deficit angle. These results illustrate the utility of quantum correlations as diagnostic tools for probing geometric properties beyond the classical regime and offer a complementary perspective on the interplay between spacetime structure and quantum entanglement.