Topological Complexity in AdS3/CFT2

@article{Abt2018TopologicalCI,
  title={Topological Complexity in AdS3/CFT2},
  author={Raimond Abt and Johanna Erdmenger and Haye Hinrichsen and Charles M. Melby-Thompson and Ren'e Meyer and Christian Northe and Ignacio A. Reyes},
  journal={Fortschritte der Physik},
  year={2018},
  volume={66}
}
We consider subregion complexity within the AdS3/CFT2 correspondence. We rewrite the volume proposal, according to which the complexity of a reduced density matrix is given by the spacetime volume contained inside the associated Ryu‐Takayanagi (RT) surface, in terms of an integral over the curvature. Using the Gauss‐Bonnet theorem we evaluate this quantity for general entangling regions and temperature. In particular, we find that the discontinuity that occurs under a change in the RT surface… 

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