A scattering amplitude in Conformal Field Theory
Marc Gillioz, Marco Meineri, João Penedones
Abstract
A bstract We define form factors and scattering amplitudes in Conformal Field Theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as p 2 → 0. In particular, we study a form factor F ( s, t, u ) obtained from a four-point function of identical scalar primary operators. We show that F is crossing symmetric, analytic and it has a partial wave expansion. We illustrate our findings in the 3d Ising model, perturbative fixed points and holographic CFTs.
Topics & Concepts
PhysicsCrossingScattering amplitudeConformal field theorySingularityQuantum electrodynamicsConformal mapMathematical physicsAmplitudeCorrelation function (quantum field theory)Scalar fieldScalar (mathematics)Form factor (electronics)Conformal symmetryScatteringField theory (psychology)Ising modelFourier transformScattering theoryQuantum mechanicsQuantum field theoryConformal anomalyField (mathematics)S-matrixPerturbation theory (quantum mechanics)Beta function (physics)Partial wave analysisBoundary conformal field theoryScalar field theoryOptical theoremHolographyScattering lengthEssential singularityFunction (biology)Wave functionPrimary fieldFourier analysisBlack Holes and Theoretical PhysicsQuantum Chromodynamics and Particle InteractionsAlgebraic structures and combinatorial models