The tricritical Ising CFT and conformal bootstrap

TL;DR

This paper explores the tricritical Ising conformal field theory using the numerical conformal bootstrap across various dimensions, identifying consistent parameter regions and reviewing existing perturbative and exact results.

Contribution

It applies the conformal bootstrap method to the tricritical Ising CFT in multiple dimensions, finding new bootstrap islands and connecting perturbative and exact results.

Findings

Bootstrap islands in d=2.75 and d=2.5 consistent with interpolations

Inconclusive bootstrap results in d=2 and d=2.25

Survey of perturbative spectrum and literature review

Abstract

The tricritical Ising CFT is the IR fixed-point of $\lambda\phi^6$ theory. It can be seen as a one-parameter family of CFTs connecting between an $\varepsilon$-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 $\{\phi\sim\sigma,\phi^2\sim \epsilon,\phi^3\sim\sigma'\}$, 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.