  We consider a class of tripartite systems for which two $d$-dimensional QFTs
are cross-coupled via a third $d+1$-dimensional "messenger" QFT. We analyse in
detail the example of a pair of one-dimensional matrix quantum mechanics,
coupled via a two-dimensional theory of the BF-type and compute its partition
function and simple correlators. This construction is extendible in higher
dimensions, using a Chern-Simons "messenger" theory. In all such examples, the
exact partition function acquires a form, speculated to correspond to systems
dual to Euclidean wormholes and the cross correlators are sufficiently soft and
consistent with analogous gravitational calculations. Another variant of the
tripartite system is studied, where the messenger theory is described by a
non-self-interacting (matrix)-field, reaching similar conclusions. While the
Euclidean theories we consider are perfectly consistent, the two possible
analytic continuations into Lorentzian signature (messenger vs. boundary QFT
directions) of the tripartite models, reveal physical features and
"pathologies" resembling those of the expected Lorentzian gravitational
backgrounds.
