Abstract
In this paper we discuss behaviors of entanglement entropy between two interacting CFTs and its holographic interpretation using the AdS/CFT correspondence. We explicitly perform analytical calculations of entanglement entropy between two free scalar field theories which are interacting with each other in both static and time-dependent ways. We also conjecture a holographic calculation of entanglement entropy between two interacting $\mathcal{N}=4$ super Yang-Mills theories by introducing a minimal surface in the S$^5$ direction, instead of the AdS$_5$ direction. This offers a possible generalization of holographic entanglement entropy.
Highlights
In most of literature, the entanglement entropy is geometrically defined by separating the spatial manifold into the subsystem A and B
The main purpose of this paper is to analyze entanglement entropy between two CFTs which live in a common spacetime and interacting with each other, described by the action of the form: S = dxd [LCFT1 + LCFT2 + Lint]
We can define the entanglement entropy between CFT1 and CFT2 by tracing out the total density matrix ρtot over either of them: Sent = −Trρ1 log ρ1, ρ1 = TrHCFT2 [ρtot]
Summary
The entanglement entropy is geometrically defined by separating the spatial manifold into the subsystem A and B. We can define the entanglement entropy between CFT1 and CFT2 by tracing out the total density matrix ρtot over either of them: Sent = −Trρ log ρ1, ρ1 = TrHCFT2 [ρtot]. It is obvious that if there are no interactions between them, Sent is vanishing This entanglement entropy may offer us a universal measure of strength of interactions. Such a problem was already analyzed in [21,22,23,24] mainly from condensed matter viewpoints. We will present two different but equivalent methods of calculations: (i) a real time formalism based on wave functionals and (ii) an Euclidean replica formalism using boundary states Owing to these methods, we will study the time evolutions of entanglement entropy when we turn on interactions instantaneously at a time
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