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In this paper we study the conjectural relation between confinement in aquantum field theory and the presence of a phase transition in itscorresponding entanglement entropy. We determine the sufficient conditions forthe latter and compare to the conditions for having a confining Wilson line. Wedemonstrate the relation in several examples. Superficially, it may seem thatcertain confining field theories with a non-local high energy behaviour, likethe dual of D5 branes wrapping a two-cycle, do not admit the correspondingphase transition. However, upon closer inspection we find that, through theintroduction of a regulating UV-cutoff, new eight-surface configurationsappear, that satisfy the correct concavity condition and recover the phasetransition in the entanglement entropy. We show that a local-UV-completion tothe confining non-local theories has a similar effect to that of theaforementioned cutoff.

Confinement, Phase Transitions and non-Locality in the Entanglement Entropy