We analyse the properties of Wilson loop observables for holographic gauge theories, when the dual bulk geometries have a single and/or multiple boundaries (Euclidean wormholes). Such observables lead to a generalisation and refinement of the characterisation in arXiv:2202.01372 based on the compressibility of cycles and the pinching limit of higher genus Riemann surfaces, since they carry information about the dynamics and phase structure of the dual gauge theory of an arbitrary dimensionality. Finally, we describe how backreacting correlated observables such as Wilson loops can lead to Euclidean wormhole saddles in the dual gravitational path integral, by taking advantage of a representation theoretic entanglement structure proposed in arXiv:2110.14655 and arXiv:2204.01764 .
