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 $\tau$, asking whether the complete set of bipartite RT entropies can remain exactly $\tau$-independent while the holographic $\mathtt q=4$ multi-entropy is sensitive to the twist. Within the class of configurations analyzed here, for sufficiently small $|\tau|$, we find no such regime along the symmetric line $\ell=m$: the globally minimal $\mathtt q=4$ network is itself exactly $\tau$-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.