# Boundary holographic Witten diagrams

## Abstract

In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect. Boundary CFTs allow two different de-compositions of two-point functions into conformal blocks: boundary channel and ambient channel. Building on earlier work, we derive a holographic dual of the boundary channel decomposition in terms of bulk-to-bulk propagators on lower dimensional AdS slices. In the situation in which we can treat the boundary or defect as a perturbation around pure AdS spacetime, we obtain the leading corrections to the two-point function both in boundary and ambient channel in terms of geodesic Witten diagrams which exactly reproduce the decomposition into corresponding conformal blocks on the field theory side.

- Authors:

- Univ. of Washington, Seattle, WA (United States)
- Univ. of Washington, Seattle, WA (United States); Univ. of Tokyo (Japan)

- Publication Date:

- Research Org.:
- Univ. of Washington, Seattle, WA (United States)

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

- OSTI Identifier:
- 1426868

- Grant/Contract Number:
- SC0011637

- 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: 9; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Karch, Andreas, and Sato, Yoshiki.
```*Boundary holographic Witten diagrams*. United States: N. p., 2017.
Web. doi:10.1007/JHEP09(2017)121.

```
Karch, Andreas, & Sato, Yoshiki.
```*Boundary holographic Witten diagrams*. United States. doi:10.1007/JHEP09(2017)121.

```
Karch, Andreas, and Sato, Yoshiki. Mon .
"Boundary holographic Witten diagrams". United States.
doi:10.1007/JHEP09(2017)121. https://www.osti.gov/servlets/purl/1426868.
```

```
@article{osti_1426868,
```

title = {Boundary holographic Witten diagrams},

author = {Karch, Andreas and Sato, Yoshiki},

abstractNote = {In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect. Boundary CFTs allow two different de-compositions of two-point functions into conformal blocks: boundary channel and ambient channel. Building on earlier work, we derive a holographic dual of the boundary channel decomposition in terms of bulk-to-bulk propagators on lower dimensional AdS slices. In the situation in which we can treat the boundary or defect as a perturbation around pure AdS spacetime, we obtain the leading corrections to the two-point function both in boundary and ambient channel in terms of geodesic Witten diagrams which exactly reproduce the decomposition into corresponding conformal blocks on the field theory side.},

doi = {10.1007/JHEP09(2017)121},

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

number = 9,

volume = 2017,

place = {United States},

year = {Mon Sep 25 00:00:00 EDT 2017},

month = {Mon Sep 25 00:00:00 EDT 2017}

}