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

Preprint number: CP3-Origins-2014-50 DNRF90 and DIAS-2014-50
Authors: Uri Kol (Tel Aviv University), Carlos Nunez (Swansea University & CP3-Origins & DIAS), Daniel Schofield (Swansea University), Jacob Sonnenschein (Tel Aviv University), and Michael Warschawski (Swansea University)
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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.