Study On Kinematic Space Of Quantum Extreme Surfaces

In recent years,the Ad S/CFT duality has received extensive attention as a specific realization of the holographic principle.Due to its profound connection between gravitational theory and quantum field theory,it has been widely applied in various research areas of physics.One of the latest applications is the utilization of holographic entanglement entropy and quantum extremal surfaces(QES),providing a novel solution to the problem of information loss in black holes.Subsequently,the concept of Ad S/BCFT was introduced,which involves double holography,representing the dual application of the holographic principle.With Ad S/BCFT,it becomes possible to geometrically derive the entanglement entropy of boundary conformal field theory(BCFT),where the geometric quantities correspond to the respective integration regions in kinematic space(K space).Consequently,a close connection is established between K space and CFT.In K space,a point is viewed as a geodesic line in Ad S and as an entanglement interval in CFT.K space plays a crucial role as an intermediary translator in investigating the Ad S/CFT duality,and it also plays a significant role in studies involving bulk reconstruction,MERA tensor networks,and holographic entanglement complexity.In this thesis we propose a K space description of QES,and focus on the study of entanglement entropy inequalities,mutual information,and conditional mutual information from the perspective of K space.In other words,by easily identifying the regions in K space responsible for computing these physical quantities,K space provides a more intuitive representation of entanglement entropy inequalities.Building upon this,we further employ the viewpoint of double holography to investigate the properties of entanglement inequalities in arbitrary regions,discovering that K space enables convenient calculation of the contributions from the bulk to holographic entanglement entropy.Lastly,we delve into the fine structure of entanglement entropy,which involves the concept of contour functions.Using K space,we demonstrate a conjecture with ease,namely,that the contribution of a subregion within an entanglement region to the total entanglement entropy can be expressed as a linear combination of the entanglement entropies of individual intervals within the entanglement region.