HET Journal club: Raimond Abt – University of Copenhagen

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.