## Einstein gravity 3-point functions from conformal field theory

## Abstract

We report on stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter implies that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions $$\langle$$T T T $$\rangle$$, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

- Authors:

- Cornell Univ., Ithaca, NY (United States)

- Publication Date:

- Research Org.:
- Cornell Univ., Ithaca, NY (United States)

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

- OSTI Identifier:
- 1512448

- Grant/Contract Number:
- SC0014123

- 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: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Afkhami-Jeddi, Nima, Hartman, Thomas, Kundu, Sandipan, and Tajdini, Amirhossein. Einstein gravity 3-point functions from conformal field theory. United States: N. p., 2017.
Web. doi:10.1007/jhep12(2017)049.
```

```
Afkhami-Jeddi, Nima, Hartman, Thomas, Kundu, Sandipan, & Tajdini, Amirhossein. Einstein gravity 3-point functions from conformal field theory. United States. doi:10.1007/jhep12(2017)049.
```

```
Afkhami-Jeddi, Nima, Hartman, Thomas, Kundu, Sandipan, and Tajdini, Amirhossein. Tue .
"Einstein gravity 3-point functions from conformal field theory". United States. doi:10.1007/jhep12(2017)049. https://www.osti.gov/servlets/purl/1512448.
```

```
@article{osti_1512448,
```

title = {Einstein gravity 3-point functions from conformal field theory},

author = {Afkhami-Jeddi, Nima and Hartman, Thomas and Kundu, Sandipan and Tajdini, Amirhossein},

abstractNote = {We report on stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter implies that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions $\langle$T T T $\rangle$, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.},

doi = {10.1007/jhep12(2017)049},

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

number = 12,

volume = 2017,

place = {United States},

year = {2017},

month = {12}

}