Finite cutoff CFT's and composite operators

Abstract

Recently a conformally invariant action describing the Wilson-Fisher fixed point in D=4−ϵ dimensions in the presence of a finite UV cutoff was constructed [44]. In the present paper we construct two composite operator perturbations of this action with definite scaling dimension also in the presence of a finite cutoff. Thus the operator (as well as the fixed point action) is well defined at all momenta 0≤p≤∞ and at low energies they reduce to ∫xϕ2 and ∫xϕ4 respectively. The construction includes terms up to O(ϵ2). In the presence of a finite cutoff they mix with higher order ∫xϕn operators. The dimensions are also calculated to this order and agree with known results.