  We consider the holographic candidate for the entanglement of purification
$E_P$, given by the minimal cross sectional area of an entanglement wedge
$E_W$. The $E_P$ is generally very complicated quantity to obtain in field
theories, thus to establish the conjectured relationship one needs to test if
$E_W$ and $E_P$ share common features. In this paper the entangling regions we
consider are slabs, concentric spheres, and creases in field theories in
Minkowski space. The latter two can be mapped to regions in field theories
defined on spheres, thus corresponding to entangled caps and orange slices,
respectively. We work in general dimensions and for slabs we also consider
field theories at finite temperature and confining theories. We find that
$E_W$, similarly to holographic mutual information, is not a monotonic function
of a scale. We also study a full ten-dimensional string theory geometry dual to
a non-trivial RG flow of a three-dimensional Chern-Simons matter theory coupled
to fundamentals. We show that also in this case $E_W$ behaves non-trivially,
which if connected to $E_P$, lends further support that the system can undergo
purification simply by expansion or reduction in scale.

High Energy Physics - Theory