Confinement, phase transitions and non-locality in the entanglement entropy

Abstract

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 behavior, 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.

Schwinger effect and entanglement entropy in confining geometries

“…In section 5 we look at the phase diagrams of the entanglement entropy of a strip, similar to the calculation in [16] , [17] and [18]. Klebanov, Kutasov and Murugan found a generalization of RyuTakayanagi relation for the non-conformal geometries [16].…”

“…Other methods could be using the ideas in [28] or [29], to study the entanglement entropy of local operators or localizes excited states in each background. But here we follow the calculation of [17] and [16] to find the entanglement entropy of a strip in each confining geometries. Also the entanglement entropy of multiple strips can be calculated similar to [30].…”

“…Using the KKM equation [16], [17] the EE for the connected solution is 4) and the EE of the disconnected solution is given by 5) and the length of the line segment of the connected solution is…”

“…For the case of Witten QCD background similar to [17], one can define the functions α(u), β(u) and H(u) as…”

“…Klebanov, Kutasov and Murugan found a generalization of RyuTakayanagi relation for the non-conformal geometries [16]. Then in [17], the authors presented the plots of the phase diagram for geometries constructed by Dp brane compactified on a circle which are the generalization of the Witten-QCD model. They have found a butterfly shape and a double valuedness in the phase diagram of these confining geometries.…”