# Butterfly velocities for holographic theories of general spacetimes

## Abstract

The butterfly velocity characterizes the spread of correlations in a quantum system. Recent work has provided a method of calculating the butterfly velocity of a class of boundary operators using holographic duality. Utilizing this and a presumed extension of the canonical holographic correspondence of AdS/CFT, we investigate the butterfly velocities of operators with bulk duals living in general spacetimes. We analyze some ubiquitous issues in calculating butterfly velocities using the bulk effective theory, and then extend the previously proposed method to include operators in entanglement shadows. Here in this paper, we explicitly compute butterfly velocities for bulk local operators in the holographic theory of flat Friedmann-Robertson-Walker spacetimes and find a universal scaling behavior for the spread of operators in the boundary theory, independent of dimension and fluid components. This result may suggest that a Lifshitz field theory with z = 4 is the appropriate holographic dual for these spacetimes.

- Authors:

- Univ. of California, Berkeley, CA (United States). Berkeley Center for Theoretical Physics, Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Tokyo (Japan). Kavli Inst. for the Physics and Mathematics of the Universe (WPI)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Tokyo (Japan). Kavli Inst. for the Physics and Mathematics of the Universe (WPI)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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

- OSTI Identifier:
- 1421810

- Grant/Contract Number:
- AC02-05CH11231; 15H05895; PHY-1521446

- 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: 10; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 79 ASTRONOMY AND ASTROPHYSICS; Models of Quantum Gravity; AdS-CFT Correspondence; Holography and condensed matter physics (AdS/CMT)

### Citation Formats

```
Nomura, Yasunori, and Salzetta, Nico.
```*Butterfly velocities for holographic theories of general spacetimes*. United States: N. p., 2017.
Web. doi:10.1007/JHEP10(2017)187.

```
Nomura, Yasunori, & Salzetta, Nico.
```*Butterfly velocities for holographic theories of general spacetimes*. United States. doi:10.1007/JHEP10(2017)187.

```
Nomura, Yasunori, and Salzetta, Nico. Sun .
"Butterfly velocities for holographic theories of general spacetimes". United States.
doi:10.1007/JHEP10(2017)187. https://www.osti.gov/servlets/purl/1421810.
```

```
@article{osti_1421810,
```

title = {Butterfly velocities for holographic theories of general spacetimes},

author = {Nomura, Yasunori and Salzetta, Nico},

abstractNote = {The butterfly velocity characterizes the spread of correlations in a quantum system. Recent work has provided a method of calculating the butterfly velocity of a class of boundary operators using holographic duality. Utilizing this and a presumed extension of the canonical holographic correspondence of AdS/CFT, we investigate the butterfly velocities of operators with bulk duals living in general spacetimes. We analyze some ubiquitous issues in calculating butterfly velocities using the bulk effective theory, and then extend the previously proposed method to include operators in entanglement shadows. Here in this paper, we explicitly compute butterfly velocities for bulk local operators in the holographic theory of flat Friedmann-Robertson-Walker spacetimes and find a universal scaling behavior for the spread of operators in the boundary theory, independent of dimension and fluid components. This result may suggest that a Lifshitz field theory with z = 4 is the appropriate holographic dual for these spacetimes.},

doi = {10.1007/JHEP10(2017)187},

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

number = 10,

volume = 2017,

place = {United States},

year = {Sun Oct 01 00:00:00 EDT 2017},

month = {Sun Oct 01 00:00:00 EDT 2017}

}

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