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

TL;DR

This paper applies the analytic functional approach to conformal field theories related to mean field theory and the Wilson-Fisher fixed point, deriving OPE coefficients constrained by crossing symmetry up to first order in epsilon.

Contribution

It introduces a novel application of analytic functionals to derive OPE coefficients in specific conformal field theories, extending previous methods.

Findings

Derived OPE coefficients constrained by crossing symmetry.

Extended analysis to first order in epsilon.

Provided new insights into 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 $\epsilon$.