Eur. Phys. J. C (2018) 78: 105
https://doi.org/10.1140/epjc/s10052-018-5545-2

Regular Article - Theoretical Physics

Entanglement from dissipation and holographic interpretation

¹ IFLP-CONICET CC 67, 1900, La Plata, Buenos Aires, Argentina
² Instituto de Física, Universidade Federal da Bahia, Campus Universitário de Ondina, Salvador, BA, CEP: 40210-340, Brazil
³ Universidade Federal da Integração Latino-Americana, Instituto Latino-Americano de Ciências da Vida e da Natureza, Av. Tancredo Neves 6731 bloco 06, Foz do Iguaçu, PR, CEP: 85867-970, Brazil

^* e-mail: dafni.marchioro@unila.edu.br
^** e-mail: dafnifernanda@gmail.com

Received: 29 June 2017
Accepted: 14 January 2018
Published online: 5 February 2018

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).