Unitarity and the Holographic S-Matrix

Journal Article · Tue Aug 28 00:00:00 EDT 2012 · arXiv:1112.4845

DOI:https://doi.org/10.1007/JHEP10(2012)032· OSTI ID:1049764

Fitzpatrick, A Liam; Kaplan, Jared

The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams. To demonstrate these facts we introduce some new techniques for the analysis of conformal field theories. Chief among these is a method for conglomerating local primary operators O{sub 1} and O{sub 2} to extract the contribution of an individual primary O{sub {Delta},{ell}} in their OPE. This provides a method for isolating the contribution of specific conformal blocks which we use to prove an important relation between certain conformal block coefficients and anomalous dimensions. These techniques make essential use of the simplifications that occur when CFT correlators are expressed in terms of a Mellin amplitude.

• Research Organization: SLAC National Accelerator Laboratory (SLAC)
• Sponsoring Organization: US DOE Office of Science (DOE SC)
• DOE Contract Number: AC02-76SF00515
• OSTI ID: 1049764
• Report Number(s): SLAC-PUB-14979; arXiv:1112.4845
• Journal Information: arXiv:1112.4845, Journal Name: arXiv:1112.4845
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANOMALOUS DIMENSION
FEYNMAN DIAGRAM
FIELD THEORIES
OPTICAL THEOREM
PERTURBATION THEORY
Phenomenology-HEP
Theory-HEP
HEPPH
HEPTH
S MATRIX
UNITARITY