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.

Rényi entropy and conformal defects

Bianchi L.;Meineri M.;
2016-01-01

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.
2016
2016
7
1
38
Anomalies in Field and String Theories; Conformal and W Symmetry; Space-Time Symmetries; Spacetime Singularities
Bianchi L.; Meineri M.; Myers R.C.; Smolkin M.
File in questo prodotto:
File Dimensione Formato  
Bianchi2016_Article_RényiEntropyAndConformalDefect.pdf

Accesso aperto

Tipo di file: PDF EDITORIALE
Dimensione 684.89 kB
Formato Adobe PDF
684.89 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1849056
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 67
  • ???jsp.display-item.citation.isi??? 66
social impact