Application of analytic functionals to mean field theory and Wilson-Fisher fixed point

Abstract: We consider application of the analytic functional approach to the conformal field theories associated with mean field theory and Wilson-Fisher fixed point. We study the constraints imposed by the crossing symmetry on the coefficients of the operator product expansion. Making use of these constraints along with a few other additional inputs, we obtain expressions of the coefficients of the operator product expansion up to first order of $ε$.