On the ϕ 3 theory above six dimensions

Abstract

Abstract We study the scalar φ 3 theory above six dimensions. The beta function β g = − ∈ g − 3 4 g 3 $$ \beta (g)=-\in g-\frac{3}{4}{g}^3 $$ in d = 6 − 2ϵ 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.

Keywords

• Conformal Field Theory
• Field Theories in Higher Dimensions