## The gravity duals of modular Hamiltonians

## Abstract

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region.

- Authors:

- Harvard Univ., Cambridge, MA (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1362133

- Grant/Contract Number:
- SC0012567

- 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: 9; 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; field theories in higher dimensions

### Citation Formats

```
Jafferis, Daniel L., and Suh, S. Josephine. The gravity duals of modular Hamiltonians. United States: N. p., 2016.
Web. doi:10.1007/JHEP09(2016)068.
```

```
Jafferis, Daniel L., & Suh, S. Josephine. The gravity duals of modular Hamiltonians. United States. doi:10.1007/JHEP09(2016)068.
```

```
Jafferis, Daniel L., and Suh, S. Josephine. Mon .
"The gravity duals of modular Hamiltonians". United States. doi:10.1007/JHEP09(2016)068. https://www.osti.gov/servlets/purl/1362133.
```

```
@article{osti_1362133,
```

title = {The gravity duals of modular Hamiltonians},

author = {Jafferis, Daniel L. and Suh, S. Josephine},

abstractNote = {In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region.},

doi = {10.1007/JHEP09(2016)068},

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

number = 9,

volume = 2016,

place = {United States},

year = {2016},

month = {9}

}

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Cited by: 14 works

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