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Nonperturbative Mellin Amplitudes: Existence, Properties, Applications

Joao Penedones, Joao A. Silva, Alexander Zhiboedov

23/12/19 Published in : arXiv:1912.11100

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 use them to constrain holographic theories. To our great surprise, we find that a free massive scalar minimally coupled to gravity does not admit UV completion as a consistent theory of quantum gravity within a certain range of masses!

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  • String Theory
  • Field Theory

Strong and weak lensing of Gravitational Waves: a semi-analytical approach

Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders

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