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 $$\epsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math> .