Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 3, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP03(2020)061
Keywords
AdS-CFT Correspondence; Conformal Field Theory; Scattering Amplitudes
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Funding
- Perimeter Institute for Theoretical Physics
- Government of Canada through the Department of Innovation, Science and Economic Development
- Province of Ontario through the Ministry of Research and Innovation
- Sherman Fairchild Foundation
- Simons Foundation [488657]
- U.S. Department of Energy, Office of Science, Office of High Energy Physics [DE-SC0011632]
- National Science Foundation [PHY-1607611]
- Walter Burke Institute for Theoretical Physics
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We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of [1] that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams - we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams - in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout.
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