Abstract
In this work we study a dissipative field theory where the dissipation process is manifestly related to dynamical entanglement and put it in the holographic context. Such endeavour is realized by further development of a canonical approach to study quantum dissipation, which consists of doubling the degrees of freedom of the original system by defining an auxiliary one. A time dependent entanglement entropy for the vacumm state is calculated and a geometrical interpretation of the auxiliary system and the entropy is given in the context of the AdS/CFT correspondence using the Ryu–Takayanagi formula. We show that the dissipative dynamics is controlled by the entanglement entropy and there are two distinct stages: in the early times the holographic interpretation requires some deviation from classical General Relativity; in the later times the quantum system is described as a wormhole, a solution of the Einstein’s equations near to a maximally extended black hole with two asymptotically AdS boundaries. We focus our holographic analysis in this regime, and suggest a mechanism similar to teleportation protocol to exchange (quantum) information between the two CFTs on the boundaries (see Maldacena et al. in Fortschr Phys 65(5):1700034, arXiv:1704.05333 [hep-th], 2017).
Highlights
The AdS/Conformal Field Theory (CFT) correspondence is the most successful application of the holographic principle, and it plays a very important role in the study of the non perturbative sector of a class of Yang–Mills theories
By putting forward the Feshbach–Ticochinski approach in [22], it was realized a relationship between the canonical quantization of the damped harmonic oscillator and the Thermo Field Dynamics (TFD) formalism, where the damped harmonic oscillator was interpreted as the thermal vacuum and the TFD entropy operator appears naturally as the entanglement entropy operator, in a suitable extension to quantum fields
We have studied a close relation between dissipation and entanglement in the context of AdS/CFT correspondence
Summary
The AdS/CFT correspondence is the most successful application of the holographic principle, and it plays a very important role in the study of the non perturbative sector of a class of Yang–Mills theories. By putting forward the Feshbach–Ticochinski approach in [22], it was realized a relationship between the canonical quantization of the damped harmonic oscillator and the TFD formalism, where the damped harmonic oscillator was interpreted as the thermal vacuum and the TFD entropy operator appears naturally as the entanglement entropy operator, in a suitable extension to quantum fields Following these ideas, we are going to use in this work the RT formula to give a holographic interpretation of the relationship between entanglement and dissipation, concerning conformal field theories at zero and finite temperature. It will be shown that the time dependent entanglement entropy derived here demands that the original metric is not BTZ, but a sort of Vaidya solution in the adiabatic approximation; that is, a BTZ black hole with a slowly time dependent mass Keeping this scenario in mind, the RT formula allows to find a natural relationship between dissipation, entanglement, thermodynamics and black hole physics. This work is organized as follows: in Sect. 2 we present the dissipative model; in Sects. 3 and 4 the time dependent entropy is canonically computed; in Sect. 5 we show how we deal with the time dependence of the entropy in holographic computations; in Sect. 6 the holographic model is constructed; and Sect. 7 is devoted to the conclusions
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