Rényi entropy and conformal defects

Lorenzo Bianchi*, Marco Meineri, Robert C. Myers, Michael Smolkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

67 Scopus citations

Abstract

We propose a field theoretic framework for calculating the dependence of Rényi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Rényi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Rényi entropy arising from small deformations of a spherical entangling surface, extending Mezei’s results for the entanglement entropy.

Original languageAmerican English
Article number76
JournalJournal of High Energy Physics
Volume2016
Issue number7
DOIs
StatePublished - 1 Jul 2016
Externally publishedYes

Bibliographical note

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

Keywords

  • Anomalies in Field and String Theories
  • Conformal and W Symmetry
  • Space-Time Symmetries
  • Spacetime Singularities

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