# Equivalent equations of motion for gravity and entropy

## Abstract

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

- Authors:

- Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics. Physics Dept.
- SLAC National Accelerator Lab., Menlo Park, CA (United States). Theory Group

- Publication Date:

- Research Org.:
- Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE; The Netherlands Organisation for Scientific Research (NWO) (Netherlands)

- OSTI Identifier:
- 1353113

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Conformal Field Theory

### Citation Formats

```
Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, and Sully, James.
```*Equivalent equations of motion for gravity and entropy*. United States: N. p., 2017.
Web. doi:10.1007/JHEP02(2017)004.

```
Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, & Sully, James.
```*Equivalent equations of motion for gravity and entropy*. United States. doi:10.1007/JHEP02(2017)004.

```
Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, and Sully, James. Wed .
"Equivalent equations of motion for gravity and entropy". United States.
doi:10.1007/JHEP02(2017)004. https://www.osti.gov/servlets/purl/1353113.
```

```
@article{osti_1353113,
```

title = {Equivalent equations of motion for gravity and entropy},

author = {Czech, Bartlomiej and Lamprou, Lampros and McCandlish, Samuel and Mosk, Benjamin and Sully, James},

abstractNote = {We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.},

doi = {10.1007/JHEP02(2017)004},

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

number = 2,

volume = 2017,

place = {United States},

year = {Wed Feb 01 00:00:00 EST 2017},

month = {Wed Feb 01 00:00:00 EST 2017}

}

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Cited by: 4 works

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