3 research outputs found
Unitarity and the Holographic S-Matrix
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 to extract the contribution of an individual primary 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.Comment: 33+12 pages, 6 figures; v2: typos corrected, some clarifications
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Analyticity and the Holographic S-Matrix
We derive a simple relation between the Mellin amplitude for AdS/CFT
correlation functions and the bulk S-Matrix in the flat spacetime limit,
proving a conjecture of Penedones. As a consequence of the Operator Product
Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic
function with simple poles on the real axis. This provides a powerful and
suggestive handle on the locality vis-a-vis analyticity properties of the
S-Matrix. We begin to explore analyticity by showing how the familiar poles and
branch cuts of scattering amplitudes arise from the holographic description.
For this purpose we compute examples of Mellin amplitudes corresponding to
1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime
limit of conformal blocks, implicitly relating the S-Matrix program to the
Bootstrap program for CFTs. We use this connection to show how the existence of
small black holes in AdS leads to a universal prediction for the conformal
block decomposition of the dual CFT.Comment: 28+15 pages, 7 figures; v2: typos correcte