Abstract
We analyze the holographic entanglement entropy in a soliton background with Wilson lines and derive a relation analogous to the first law of thermodynamics. The confinement/deconfinement phase transition occurs due to the competition of two minimal surfaces. The entropic c function probes the confinement/deconfinement phase transition. It is sensitive to the degrees of freedom (DOF) smaller than the size of a spatial circle. When the Wilson line becomes large, the entropic c function becomes non-monotonic as a function of the size and does not satisfy the usual c-theorem. We analyze the entanglement entropy for a small subregion and the relation analogous to the first law of thermodynamics. For the small amount of Wilson lines, the excited amount of the entanglement entropy decreases from the ground state. It reflects that confinement decreases degrees of freedom. We finally discuss the second order correction of the holographic entanglement entropy.
Highlights
The entanglement entropy of a subsystem becomes a nonlocal quantity in contrast to correlation functions in quantum field theories [1,2]
The phase transition occurs at the scale lM0 ∼ 1 due to the competition of two minimal surfaces as analogous to [8]
Our result implies that the dual quantum field theory (QFT) is a confining theory and there is no correlation at a large distance due to the mass gap and confinement
Summary
The entanglement entropy of a subsystem becomes a nonlocal quantity in contrast to correlation functions in quantum field theories [1,2]. We analyze a phase transition as well as thermodynamic properties of the holographic entanglement entropy in a solitonic background with a background gauge field. We consider both small and large subregions of the entanglement entropy. We compute the entanglement entropy and the entropic C function The latter becomes a nice probe of the confinement/deconfinement phase transition. As a by-product, we work out the generic formula for the second order correction to the holographic entanglement entropy with contributions from the deformation of the entangling surface. In Appendix B, we compute the second order correction to the holographic entanglement entropy with spherical entanglement surface
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