Entanglement and RG in the O(N) vector model

Chris Akers, Omer Ben-Ami, Vladimir Rosenhaus*, Michael Smolkin, Shimon Yankielowicz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Abstract: We consider the large N interacting vector O(N) model on a sphere in 4 − ϵ Euclidean dimensions. The Gaussian theory in the UV is taken to be either conformally or non-conformally coupled. The endpoint of the RG flow corresponds to a conformally coupled scalar field at the Wilson-Fisher fixed point. We take a spherical entangling surface in de Sitter space and compute the entanglement entropy everywhere along the RG trajectory. In 4 dimensions, a free non-conformal scalar has a universal area term scaling with the logarithm of the UV cutoff. In 4 − ϵ dimensions, such a term scales as 1/ϵ. For a non-conformal scalar, a 1/ϵ term is present both at the UV fixed point, and its vicinity. For flow between two conformal fixed points, 1/ϵ terms are absent everywhere. Finally, we make contact with replica trick calculations. The conical singularity gives rise to boundary terms residing on the entangling surface, which are usually discarded. Consistency with our results requires they be kept. We argue that, in fact, this conclusion also follows from the work of Metlitski, Fuertes, and Sachdev, which demonstrated that such boundary terms will be generated through quantum corrections.

Original languageAmerican English
Article number2
JournalJournal of High Energy Physics
Volume2016
Issue number3
DOIs
StatePublished - 1 Mar 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016, The Author(s).

Keywords

  • Conformal and W Symmetry
  • Global Symmetries
  • Renormalization Group

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