We posit a geometrical description of the entanglement of purification for
subregions in a holographic CFT. The bulk description naturally generalizes the
two-party case and leads to interesting inequalities among multi-party
entanglements of purification that can be geometrically proven from the
conjecture. Further, we study the relationship between holographic
entanglements of purification in locally-AdS3 spacetimes and entanglement
entropies in multi-throated wormhole geometries constructed via quotienting by
isometries. In particular, we derive new holographic inequalities for
geometries that are locally AdS3 relating entanglements of purification for
subregions and entanglement entropies in the wormhole geometries.Comment: 23 pages, 12 figures; v2 added references; v3 fixed inequality
direction in Eq.(2), expanded discussion - reflects published versio
