  In this paper we study the conjectural relation between confinement in a
quantum field theory and the presence of a phase transition in its
corresponding entanglement entropy. We determine the sufficient conditions for
the latter and compare to the conditions for having a confining Wilson line. We
demonstrate the relation in several examples. Superficially, it may seem that
certain confining field theories with a non-local high energy behaviour, like
the dual of D5 branes wrapping a two-cycle, do not admit the corresponding
phase transition. However, upon closer inspection we find that, through the
introduction of a regulating UV-cutoff, new eight-surface configurations
appear, that satisfy the correct concavity condition and recover the phase
transition in the entanglement entropy. We show that a local-UV-completion to
the confining non-local theories has a similar effect to that of the
aforementioned cutoff.
