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.

The zero-Hamiltonian problem, present in reparametrization invariant systems, is solved for the 2D induced gravity model. Working with methods developed by Henneaux, Teitelboim, and Vergara we find, systematically, reduced phase-space physics, generated by an effective Hamiltonian obtained after complete gauge fixing.

In this work the pure spinor formulation of the superstring is used to study quantum corrections to the left current OPE algebra of the coset P SU (2, 2|4)/SO(4, 1) × SO(5) sigma model, which describes the superstring dynamics in the AdS 5 × S 5 background. In particular, the one loop corrections to the simple poles of the bosonic currents are computed. Unlike the case of the double poles, we show that the simple poles suffer corrections, which are important since the simple poles contribute to the four point amplitudes. We show that the only contribution to the simple poles comes from the pure spinor Lorentz currents. * 1 The classical integrability of the AdS 5 × S 5 sigma model was established in the paper [7] for Green-Schwarz-Metsaev-Tseytlin action and in [8] for the pure spinor description. Using cohomological and algebraic renormalization techniques, Berkovits argued that the sigma model still has an infinite number of conserved charges when quantum effects are taken into account [3]. A detailed study of the transfer matrix of the worldsheet was done in [9], where it was shown to be a well defined operator in quantum theory. The literature on this subject is very large, and we did not attempt to give a list of references.The reader can see a list of references in [10,11].

Based on Maldacena's description of an eternal anti-de Sitter (AdS) black hole, we reassess the thermo field dynamics (TFD) formalism in the context of the AdS/CFT correspondence. The model studied here involves the maximally extended AdS-Schwarschild solution and two (noninteracting) copies of the conformal field theory (CFT) associated to the global AdS spacetime, along with an extension of the string by imposing natural gluing conditions in the horizon. We show that the gluing conditions in the horizon define a string boundary state which is identified with the TFD thermal vacuum, globally defined in the Kruskal extension of the AdS black hole. We emphasize the connection of this picture with unitary SUð1; 1Þ TFD formulation, and we show that information about the bulk and the conformal boundary is present in the SUð1; 1Þ parameters. Using the unitary SUð1; 1Þ TFD formulation, a canonical prescription for calculating the world sheet real time thermal Green's function is made, and the entropy associated with the entanglement of the two CFT's is calculated.

In another application of the methods of Henneaux, Teitelboim, and Vergara developed for diffeomorphisms invariant models, the CGHS theory of 2D black holes is focused in order to obtain the true degrees of freedom, the simplectic structure and the effective Hamiltonian that rules the dynamics in reduced phase-space.