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Title: Witten diagrams revisited: the AdS geometry of conformal blocks

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.
 [1] ;  [1] ;  [2] ;  [1]
  1. Univ. of California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
  2. Princeton Univ., NJ (United States). Dept. of Physics
Publication Date:
OSTI Identifier:
Grant/Contract Number:
FG02-91ER40671; NSF PHY11-25915; PHY-1313986
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
Springer Berlin
Research Org:
Princeton Univ., NJ (United States)
Sponsoring Org:
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS AdS-CFT correspondence; conformal and W symmetry