Comments on holographic complexity

Dean Carmi, Robert C. Myers, Pratik Rath

Research output: Contribution to journalArticlepeer-review


We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture. In particular, we examine the structure of the UV divergences appearing in these quantities, and show that the coefficients can be written as local integrals of geometric quantities in the boundary. We also consider extending these conjectures to evaluate the complexity of the mixed state produced by reducing the pure global state to a specific subregion of the boundary time slice. The UV divergences in this subregion complexity have a similar geometric structure, but there are also new divergences associated with the geometry of the surface enclosing the boundary region of interest. We discuss possible implications arising from the geometric nature of these UV divergences.

Original languageEnglish
Article number118
JournalJournal of High Energy Physics
Issue number3
StatePublished - 1 Mar 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, The Author(s).


  • AdS-CFT Correspondence
  • Classical Theories of Gravity
  • Gauge-gravity correspondence

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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