<p>The tricritical Ising CFT is the IR fixed-point of <i>λϕ</i><sup>6</sup> theory. It can be seen as a one-parameter family of CFTs connecting between an <i>ε</i>-expansion near the upper critical dimension 3 and the exactly solved minimal model in <i>d</i> = 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 {<i>ϕ</i> ~ <i>σ</i>, <i>ϕ</i><sup>2</sup> ~ <i>ϵ</i>, <i>ϕ</i><sup>3</sup> ~ <i>σ</i><sup>′</sup>}, we find three-dimensional “bootstrap islands” in <i>d</i> = 2.75 and <i>d</i> = 2.5 dimensions consistent with interpolations between the perturbative estimates and the 2d exact values. In <i>d</i> = 2 and <i>d</i> = 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.</p>

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The tricritical Ising CFT and conformal bootstrap

  • Johan Henriksson

摘要

The tricritical Ising CFT is the IR fixed-point of λϕ6 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, ϕ2 ~ ϵ, ϕ3 ~ 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.