The tricritical Ising CFT and conformal bootstrap

Abstract

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

49 pages, 19 figures. v2: version to appear in JHEP. v3: added comments on corrected beta functions

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