Topological Complexity in AdS3/CFT2

Raimond Abt, Johanna Erdmenger, Haye Hinrichsen, Charles M. Melby–Thompson, René Meyer, Christian Northe, Ignacio A. Reyes

Research output: Contribution to journalArticlepeer-review

79 Scopus citations


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 is given by a fixed topological contribution, independent of the temperature or details of the entangling region. We offer a definition and interpretation of subregion complexity in the context of tensor networks, and show numerically that it reproduces the qualitative features of the holographic computation in the case of a random tensor network using its relation to the Ising model. Finally, we give a prescription for computing subregion complexity directly in CFT using the kinematic space formalism, and use it to reproduce some of our explicit gravity results obtained at zero temperature. We thus obtain a concrete matching of results for subregion complexity between the gravity and tensor network approaches, as well as a CFT prescription.

Original languageEnglish
Article number1800034
JournalFortschritte der Physik
Issue number6
StatePublished - 1 Jun 2018
Externally publishedYes


  • AdS-CFT correspondence
  • black holes in string theory
  • gauge-gravity correspondence

ASJC Scopus subject areas

  • General Physics and Astronomy


Dive into the research topics of 'Topological Complexity in AdS3/CFT2'. Together they form a unique fingerprint.

Cite this