The tricritical Ising CFT and conformal bootstrap

A bstract The tricritical Ising CFT is the IR fixed-point of λϕ 6 theory. It can be seen as a one-parameter family of CFTs connecting between an ε -expansion near the upper critical dimension 3 and the exactly solved minimal model in d = 2. We review what is known about the tricritical Ising CFT, and study it with the numerical conformal bootstrap for various dimensions. Using a mixed system with three external operators { ϕ ~ σ , ϕ 2 ~ ϵ , ϕ 3 ~ σ ′ }, we find three-dimensional “bootstrap islands” in d = 2.75 and d = 2.5 dimensions consistent with interpolations between the perturbative estimates and the 2d exact values. In d = 2 and d = 2.25 the setup is not strong enough to isolate the theory. This paper also contains a survey of the perturbative spectrum and a review of results from the literature.