On the ϕ3 theory above six dimensions

A bstract We study the scalar φ 3 theory above six dimensions. The beta function β g = − ∈ g − 3 4 g 3 in d = 6 − 2 ϵ dimensions has a UV fixed point when ϵ < 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 ϕ 3 theory above six dimensions exist.