On shape dependence and RG flow of entanglement entropy

Igor R. Klebanov, Tatsuma Nishioka, Silviu S. Pufu, Benjamin R. Safdi

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70 Scopus citations


We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface has a conical or a wedge singularity. In (2 + 1)-dimensional field theory with a mass gap we calculate, for an arbitrary smooth entanglement contour, the expansion of the entropy in inverse odd powers of the mass. We show that the shape-dependent coefficients that arise are even powers of the extrinsic curvature and its derivatives. A useful dual construction of a (2 + 1)-dimensional theory, which allows us to exhibit these properties, is provided by the CGLP background. This smooth warped throat solution of 11-dimensional supergravity describes renormalization group flow from a conformal field theory in the UV to a gapped one in the IR. For this flow we calculate the recently introduced renormalized entanglement entropy and confirm that it is a monotonic function.

Original languageEnglish (US)
Article number1
JournalJournal of High Energy Physics
Issue number7
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • AdS-CFT correspondence
  • Field theories in lower dimensions
  • Renormalization group


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