### Abstract

We describe a holographic approach to explicitly computing the universal logarithmic contributions to entanglement and Renyi entropies for free conformal scalar and spinor fields on even-dimensional spheres. This holographic derivation proceeds in two steps: first, following Casini and Huerta, a conformal mapping to thermal entropy in a hyperbolic geometry; then identification of the hyperbolic geometry with the conformal boundary of a bulk hyperbolic space and use of an AdS/CFT holographic formula to compute the resultant functional determinant. We explicitly verify the connection with the type-A trace anomaly for the entanglement entropy, whereas the Renyi entropy is computed with the aid of the Sommerfeld formula in order to deal with a conical defect. We show that as a by-product, the log coefficient of the Renyi entropy for round spheres can be efficiently obtained as the q-analog of a procedure similar to the one found by Cappelli and D'Appollonio that rendered the type-A trace anomaly.

Original language | English |
---|---|

Article number | 105401 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 10 |

DOIs | |

Publication status | Published - 13 Mar 2015 |

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### Keywords

- entanglement
- holography
- Renyi entropy

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

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*Journal of Physics A: Mathematical and Theoretical*, vol. 48, no. 10, 105401. https://doi.org/10.1088/1751-8113/48/10/105401

**On Renyi entropy for free conformal fields : Holographic and q-analog recipes.** / Aros, R.; Bugini, F.; Diaz, D. E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On Renyi entropy for free conformal fields

T2 - Holographic and q-analog recipes

AU - Aros, R.

AU - Bugini, F.

AU - Diaz, D. E.

PY - 2015/3/13

Y1 - 2015/3/13

N2 - We describe a holographic approach to explicitly computing the universal logarithmic contributions to entanglement and Renyi entropies for free conformal scalar and spinor fields on even-dimensional spheres. This holographic derivation proceeds in two steps: first, following Casini and Huerta, a conformal mapping to thermal entropy in a hyperbolic geometry; then identification of the hyperbolic geometry with the conformal boundary of a bulk hyperbolic space and use of an AdS/CFT holographic formula to compute the resultant functional determinant. We explicitly verify the connection with the type-A trace anomaly for the entanglement entropy, whereas the Renyi entropy is computed with the aid of the Sommerfeld formula in order to deal with a conical defect. We show that as a by-product, the log coefficient of the Renyi entropy for round spheres can be efficiently obtained as the q-analog of a procedure similar to the one found by Cappelli and D'Appollonio that rendered the type-A trace anomaly.

AB - We describe a holographic approach to explicitly computing the universal logarithmic contributions to entanglement and Renyi entropies for free conformal scalar and spinor fields on even-dimensional spheres. This holographic derivation proceeds in two steps: first, following Casini and Huerta, a conformal mapping to thermal entropy in a hyperbolic geometry; then identification of the hyperbolic geometry with the conformal boundary of a bulk hyperbolic space and use of an AdS/CFT holographic formula to compute the resultant functional determinant. We explicitly verify the connection with the type-A trace anomaly for the entanglement entropy, whereas the Renyi entropy is computed with the aid of the Sommerfeld formula in order to deal with a conical defect. We show that as a by-product, the log coefficient of the Renyi entropy for round spheres can be efficiently obtained as the q-analog of a procedure similar to the one found by Cappelli and D'Appollonio that rendered the type-A trace anomaly.

KW - entanglement

KW - holography

KW - Renyi entropy

UR - http://www.scopus.com/inward/record.url?scp=84923289195&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/48/10/105401

DO - 10.1088/1751-8113/48/10/105401

M3 - Article

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 10

M1 - 105401

ER -