On ${\varphi }^3$ Theory Above Six Dimensions

Abstract

We study the scalar ${\varphi }^3$ theory above six dimensions. The beta function $\beta (g)=-\epsilon g-\frac{3}{4}{g}^3$ in $d=6-2\epsilon$ dimensions has a UV fixed point when $\epsilon <0$. Like the $O(N)$ vector models above four dimensions, such a fixed point observed perturbatively in fact corresponds to a pair of complex CFTs separated by a branch cut. Using both the numerical bootstrap method and Gliozzi's fusion rule truncation method, we argue that the fixed points of the ${\varphi }^3$ theory above six dimensions exist.

13 pages, 4 figures, typos fixed, references updated