Description
Recently, using the AdS/CFT correspondence exciting new relations are
being established between aspects of quantum information theory and of
the geometry of black holes in Anti de Sitter space-times. After a
concise review of the roles of entanglement measures such as e.g. the
entanglement entropy as well as of the computational complexity within
the AdS/CFT correspondence, I discuss the notion of subregion
complexity of a 2D critical state from three di erent viewpoints: the
AdS3/CFT2 correspondence, random tensor networks, and kinematic space.
From the AdS3/CFT2 point of view I explain how in the dis- continuity
of subregion complexity as given by the volume within the
Ryu-Takayanagi surface is related to the Euler characteristic of the
re- spective bulk regions via the Gauss-Bonnet theorem. I then discuss
how the volume of these sub regions can be calculated in kinematic
space, which is the space of geodesics on the time-slice of AdS3, and
present a new CFT expression of subregion complexity. Finally, I
present re- sults that qualitatively reproduce the discontinuity in
complexity in a tensor network approach. Based on arXiv:1710.01327
[hep-th].
