Finite Cutoff CFT's and Composite Operators

Abstract

Recently a conformally invariant action describing the Wilson-Fischer fixed point in $D=4-\epsilon$ dimensions in the presence of a {\em finite} UV cutoff was constructed \cite{Dutta}. 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 $0\le p\le \infty$ and at low energies they reduce to ${\int }_x{\varphi }^2$ and ${\int }_x{\varphi }^4$ respectively. The construction includes terms up to $O(\lamda^2)$. 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.

arXiv comment53 pages, 5 figures

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