  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 spacetime 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
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 .
