Witten diagrams revisited: the AdS geometry of conformal blocks
Abstract
Here, we develop a new method for decomposing blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a "geodesic Witten diagram", which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we also consider the case of four-point functions of scalar operators, and show how to easily reproduce existing results for the relevant conformal blocks in arbitrary dimension.
- Authors:
-
- Univ. of California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
- Princeton Univ., NJ (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1327296
- Grant/Contract Number:
- FG02-91ER40671; NSF PHY11-25915; PHY-1313986
- 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: 1; 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
Citation Formats
Hijano, Eliot, Kraus, Per, Perlmutter, Eric, and Snively, River. Witten diagrams revisited: the AdS geometry of conformal blocks. United States: N. p., 2016.
Web. doi:10.1007/JHEP01(2016)146.
Hijano, Eliot, Kraus, Per, Perlmutter, Eric, & Snively, River. Witten diagrams revisited: the AdS geometry of conformal blocks. United States. https://doi.org/10.1007/JHEP01(2016)146
Hijano, Eliot, Kraus, Per, Perlmutter, Eric, and Snively, River. Mon .
"Witten diagrams revisited: the AdS geometry of conformal blocks". United States. https://doi.org/10.1007/JHEP01(2016)146. https://www.osti.gov/servlets/purl/1327296.
@article{osti_1327296,
title = {Witten diagrams revisited: the AdS geometry of conformal blocks},
author = {Hijano, Eliot and Kraus, Per and Perlmutter, Eric and Snively, River},
abstractNote = {Here, we develop a new method for decomposing blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a "geodesic Witten diagram", which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we also consider the case of four-point functions of scalar operators, and show how to easily reproduce existing results for the relevant conformal blocks in arbitrary dimension.},
doi = {10.1007/JHEP01(2016)146},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2016,
place = {United States},
year = {Mon Jan 25 00:00:00 EST 2016},
month = {Mon Jan 25 00:00:00 EST 2016}
}
Web of Science
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