Can Multipartite Entanglement Probe Wormhole Moduli Invisible to Bipartite Entanglement?

Abstract: We ask whether multipartite entanglement can probe bulk moduli invisible to bipartite entanglement. We study this question in an explicit family of four-boundary AdS$_3$ wormholes related by a Fenchel-Nielsen twist $τ$, asking whether the complete set of bipartite RT entropies can remain exactly $τ$-independent while the holographic $\mathtt q=4$ multi-entropy is sensitive to the twist. Within the class of configurations analyzed here, for sufficiently small $|τ|$, we find no such regime along the symmetric line $\ell=m$: the globally minimal $\mathtt q=4$ network is itself exactly $τ$-independent throughout the parameter range analyzed. This conclusion is not a priori obvious: it emerges from a competition among several admissible configurations whose relative ordering changes multiple times as the geometry is varied, and persists up to the point where the bipartite RT entropies themselves become twist-sensitive.