Holographic complexity for defects distinguishes action from volume

Shira Chapman, Dongsheng Ge, Giuseppe Policastro

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


We explore the two holographic complexity proposals for the case of a 2d boundary CFT with a conformal defect. We focus on a Randall-Sundrum type model of a thin AdS 2 brane embedded in AdS 3 . We find that, using the “complexity=volume” proposal, the presence of the defect generates a logarithmic divergence in the complexity of the full boundary state with a coefficient which is related to the central charge and to the boundary entropy. For the “complexity=action” proposal we find that the logarithmically divergent term in the complexity is not influenced by the presence of the defect. This is the first case in which the results of the two holographic proposals differ so dramatically. We consider also the complexity of the reduced density matrix for subregions enclosing the defect. We explore two bosonic field theory models which include two defects on opposite sides of a periodic domain. We point out that for a compact boson, current free field theory definitions of the complexity would have to be generalized to account for the effect of zero-modes.

Original languageEnglish
Article number49
JournalJournal of High Energy Physics
Issue number5
StatePublished - 1 May 2019
Externally publishedYes


  • AdS-CFT Correspondence
  • Conformal Field Theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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