Nonperturbative Mellin amplitudes: existence, properties, applications

We argue that nonperturbative CFT correlation functions admit a Mellin amplitude representation. Perturbative Mellin representation readily follows. We discuss the main properties of nonperturbative CFT Mellin amplitudes: subtractions, analyticity, unitarity, Polyakov conditions and polynomial boundedness at infinity. Mellin amplitudes are particularly simple for largeNCFTs and 2D rational CFTs. We discuss these examples to illustrate our general discussion. We consider subtracted dispersion relations for Mellin amplitudes and use them to derive bootstrap bounds on CFTs. We combine crossing, dispersion relations and Polyakov conditions to write down a set of extremal functionals that act on the OPE data. We check these functionals using the known 3d Ising model OPE data and other known bootstrap constraints. We then apply them to holographic theories.


Published in:
Journal Of High Energy Physics, 8, 031
Year:
Aug 06 2020
Publisher:
New York, SPRINGER
ISSN:
1029-8479
Keywords:
Laboratories:




 Record created 2020-09-05, last modified 2020-10-29


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