QFT as a set of ODEs

Abstract
Anti de Sitter space is a very useful intermediate regulator to treat strongly coupled QFTs. By the state-operator map, all local observables in QFT in AdS are captured by three sets of numbers, the "QFT data": the scaling dimensions of boundary operators, their OPE coefficients, and the form factors of bulk operators. We derived a set of coupled ODEs describing how the QFT data evolves as the curvature of AdS is brought to zero, towards flat space. The ODEs do not assume weak coupling, and are thus useful to treat strongly coupled RG flows. From the asymptotic behavior of the scaling dimensions in the flat space limit, one can extract the masses of the lightest stable particles in the flat space theory. I will show preliminary results in the application of this method to 2D Ising Field Theory (with thermal and magnetic deformation) where we match to known results about the IR mass spectrum.

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