## Shape dependence of holographic Rényi entropy in general dimensions

## Abstract

We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for d = 3, · · · , 6 spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove a set of conjectures in the literature regarding the relation between the Rényi shape dependence and the conformal weight of the twist operator. As a result, we also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.

- Authors:

- Univ. Hamburg, Hamburg (Germany)
- Perimeter Institute for Theoretical Physics, Waterloo (Canada)
- Institute for Advanced Study, Princeton, NJ (United States)
- Perimeter Institute for Theoretical Physics, Waterloo (Canada); Univ. of Western Ontario, London (Canada)
- Perimeter Institute for Theoretical Physics, Waterloo (Canada); Scuola Normale Superiore, Pisa (Italy); INFN - Sezione di Pisa, Pisa (Italy)

- Publication Date:

- Research Org.:
- Univ. Hamburg, Hamburg (Germany)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1358547

- Grant/Contract Number:
- SC0009988

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 11; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT correspondence; conformal field theory; field theories in higher dimensions

### Citation Formats

```
Bianchi, Lorenzo, Chapman, Shira, Dong, Xi, Galante, Damián A., Meineri, Marco, and Myers, Robert C. Shape dependence of holographic Rényi entropy in general dimensions. United States: N. p., 2016.
Web. doi:10.1007/JHEP11(2016)180.
```

```
Bianchi, Lorenzo, Chapman, Shira, Dong, Xi, Galante, Damián A., Meineri, Marco, & Myers, Robert C. Shape dependence of holographic Rényi entropy in general dimensions. United States. doi:10.1007/JHEP11(2016)180.
```

```
Bianchi, Lorenzo, Chapman, Shira, Dong, Xi, Galante, Damián A., Meineri, Marco, and Myers, Robert C. Tue .
"Shape dependence of holographic Rényi entropy in general dimensions". United States. doi:10.1007/JHEP11(2016)180. https://www.osti.gov/servlets/purl/1358547.
```

```
@article{osti_1358547,
```

title = {Shape dependence of holographic Rényi entropy in general dimensions},

author = {Bianchi, Lorenzo and Chapman, Shira and Dong, Xi and Galante, Damián A. and Meineri, Marco and Myers, Robert C.},

abstractNote = {We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for d = 3, · · · , 6 spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove a set of conjectures in the literature regarding the relation between the Rényi shape dependence and the conformal weight of the twist operator. As a result, we also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.},

doi = {10.1007/JHEP11(2016)180},

journal = {Journal of High Energy Physics (Online)},

number = 11,

volume = 2016,

place = {United States},

year = {2016},

month = {11}

}

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