Nonperturbative Mellin amplitudes: existence, properties, applications. (English) Zbl 1454.83145
Summary: 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 large \(N\) CFTs 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.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
| 83E05 | Geometrodynamics and the holographic principle |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
Keywords:
conformal field theory; nonperturbative effects; AdS-CFT correspondence; conformal field models in string theoryReferences:
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