Finite Cutoff CFT's and Composite Operators

Abstract

Recently a conformally invariant action describing the Wilson-Fischer fixed point in D = 4−ǫ dimensions in the presence of a finite UV cutoff was constructed [41]. 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 tox φ 2 and x φ 4 respectively. The construction includes terms up to O(λ 2 ). In the presence of a finite cutoff they mix with higher order irrelevant operators. The dimensions are also calculated to this order and agree with known results.