# The AdS _{3} propagator and the fate of locality

## Abstract

We recently used Virasoro symmetry considerations to propose an exact formula for a bulk proto-field φ in AdS _{3}. In this paper we study the propagator . We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and well-defined at long distances, its perturbative expansion in ${G}_{N}=\frac{3}{2c}$ exhibits UV/IR mixing effects. If we nevertheless interpret as a probe of bulk locality, then when ${G}_{N{m}_{\varphi}}\ll 1$ locality breaks down at the new short-distance scale ${\sigma}_{\ast}\sim \sqrt[4]{{G}_{N}{R}_{\mathrm{A}\mathrm{d}\mathrm{S}}^{3}}$. For φ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality ‘breakdown’ manifests as singularities or branch cuts at spacelike separation arising from non-perturbative quantum gravitational effects.

- Authors:

- Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
- Boston Univ., MA (United States). Dept. of Physics
- Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy; Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP); Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics

- Publication Date:

- Research Org.:
- Boston Univ., MA (United States); Johns Hopkins Univ., Baltimore, MD (United States)

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

- OSTI Identifier:
- 1501934

- Grant/Contract Number:
- SC0010025; PHY-1454083

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 4; 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 and W Symmetry; conformal field theory; models of quantum gravity

### Citation Formats

```
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, and Li, Daliang.
```*The AdS3 propagator and the fate of locality*. United States: N. p., 2018.
Web. doi:10.1007/jhep04(2018)075.

```
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, & Li, Daliang.
```*The AdS3 propagator and the fate of locality*. United States. doi:10.1007/jhep04(2018)075.

```
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, and Li, Daliang. Fri .
"The AdS3 propagator and the fate of locality". United States. doi:10.1007/jhep04(2018)075. https://www.osti.gov/servlets/purl/1501934.
```

```
@article{osti_1501934,
```

title = {The AdS3 propagator and the fate of locality},

author = {Chen, Hongbin and Fitzpatrick, A. Liam and Kaplan, Jared and Li, Daliang},

abstractNote = {We recently used Virasoro symmetry considerations to propose an exact formula for a bulk proto-field φ in AdS3. In this paper we study the propagator . We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and well-defined at long distances, its perturbative expansion in G N = 3 2 c exhibits UV/IR mixing effects. If we nevertheless interpret as a probe of bulk locality, then when G N m ϕ ≪ 1 locality breaks down at the new short-distance scale σ ∗ ∼ G N R A d S 3 4 . For φ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality ‘breakdown’ manifests as singularities or branch cuts at spacelike separation arising from non-perturbative quantum gravitational effects.},

doi = {10.1007/jhep04(2018)075},

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

issn = {1029-8479},

number = 4,

volume = 2018,

place = {United States},

year = {2018},

month = {4}

}