### Fermionic localization of the schwarzian theory

The SYK model is a quantum mechanical model that has been proposed to be holographically dual to a 1 + 1-dimensional model of a quantum black hole. An emergent “gravitational” mode of this model is governed by an unusual action that has been called the Schwarzian action. It governs a reparametrization of a circle. We show that the path integral of the Schwarzian theory is one-loop exact. Here, the argument uses a method of fermionic localization, even though the model itself is purely bosonic.

- Publication Date:

- Grant/Contract Number:
- AC02-76SF00515

- Type:
- 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

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

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Field Theories in Lower Dimensions; Nonperturbative Effects

- OSTI Identifier:
- 1414835

```
Stanford, Douglas, and Witten, Edward.
```*Fermionic localization of the schwarzian theory*. United States: N. p.,
Web. doi:10.1007/JHEP10(2017)008.

```
Stanford, Douglas, & Witten, Edward.
```*Fermionic localization of the schwarzian theory*. United States. doi:10.1007/JHEP10(2017)008.

```
Stanford, Douglas, and Witten, Edward. 2017.
"Fermionic localization of the schwarzian theory". United States.
doi:10.1007/JHEP10(2017)008. https://www.osti.gov/servlets/purl/1414835.
```

```
@article{osti_1414835,
```

title = {Fermionic localization of the schwarzian theory},

author = {Stanford, Douglas and Witten, Edward},

abstractNote = {The SYK model is a quantum mechanical model that has been proposed to be holographically dual to a 1 + 1-dimensional model of a quantum black hole. An emergent “gravitational” mode of this model is governed by an unusual action that has been called the Schwarzian action. It governs a reparametrization of a circle. We show that the path integral of the Schwarzian theory is one-loop exact. Here, the argument uses a method of fermionic localization, even though the model itself is purely bosonic.},

doi = {10.1007/JHEP10(2017)008},

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

number = 10,

volume = 2017,

place = {United States},

year = {2017},

month = {10}

}