Dispersion Relation in Conformal Field Theory (Quantum Spacetime series seminar)

We propose a dispersion relation in conformal field theory which expresses the four  point correlator as an integral over its single discontinuity. Exploiting the analytic properties and crossing symmetry of the correlator, we show that in erturbative settings the correlator depends only on the spectrum of the theory, as well as the OPE coefficients of certain low twist operators and can be reconstructed  nambiguously. As an application, the correlator < Φ Φ Φ Φ >  in Φ4 theory at the Wilson-Fisher fixed point can be computed in closed form up to order ε2 in the ε expansion. At small coupling this can be thought of as an alternative way of computing the CFT correlators with some inputs using Feynman diagrams.