The Applications Of Gravity/Gauge Duality In Entanglement Entropy And Complexity In Dissipation Systems

With the use of the gravity/gauge duality,we will work in gravity theory and investigate the holographic entanglement entropy and complexity in its dual boundary theory with dissipation.The thesis consists two main parts.The first part is the evolution of the holographic entanglement entropy(HEE)and holographic complexity(HC)in thermodynamic processes.According to holography,the thermal quenching process in the boundary field theory is dual to the formation of black holes in the gravitational collapse process,so in this part we could work with Vaidya metric in the gravity theory to investigate the evolutionary properties of HEE and HC.Firstly,we will first study the evolution of HEE and HC in a charged massive BTZ black hole,in which the breaking of diffeomorphism in such theory corresponds to the momentum dissipation in the dual boundary field theory.We systematically reveal the effect of graviton mass and black hole mass on the evolutionary of HEE and HC.Secondly,it is known that the introduction of spatially dependent axion fields in the Einstein-Maxwell-axion theory can also lead to the momentum dissipation of the dual boundary theory.Thus,we will study the properties of HEE and HC in the formation of black hole in such theory.Finally,we also explore the increase of HC via the action growth by introducing probing strings in massive gravity.Our studies in the first part are realized via heavy numeric,nevertheless,for three-dimensional theories,it is possible to obtain the analytical form of entanglement entropy.Then in the second part of this thesis,we will apply quantum field theory method to study the entanglement entropy in a massive BTZ black hole coupled with a scalar field.Specifically,we use the discrete method to calculate the entanglement entropy of the scalar field in spacetime.We use the log-term to correct the entanglement entropy which we have in a black hole,and measure the graviton mass dependent fitted coefficients of each order.In the framework of the gravity/gauge duality,this thesis focuses on the entanglement properties and their dynamical processes in the boundary field theory with dissipation.Our study brings the related research closer to the real system and helps us further understand the characteristics of the holographic entanglement entropy and complexity.