HET Journal club: Raimond Abt

Speaker: Raimond Abt

Title: Holographic Subregion Complexity from Kinematic Space

Abstract: Some important new insights into the AdS/CFT correspondence and its relation to quantum information theory are provided by the concept of kinematic space. In AdS3/CFT2, kinematic space is the space of all geodesics in a constant time slice of AdS3 with endpoints at the boundary of the time slice. Kinematic space allows to find explicit expressions for geometric quantities, such as lengths of curves in the time slice of AdS3, in terms of entanglement entropies on the CFT side. Kinematic space is therefore a powerful tool to determine how quantum information aspects of the CFT are encoded in the geometry of AdS. In addition to curves, also volumes in AdS are an interesting quantity to study in context of quantum information. In particular, volumes may be used to define a concept of complexity. This is an information theoretic quantity measuring how involved a particular quantum operation is. In my talk I present an expression for volumes in terms of entanglement entropies that can be motivated by using kinematic space, and discuss its relation to complexity.