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The tricritical Ising CFT and conformal bootstrap
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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.
Forward citations
Cited by 3 Pith papers
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Redundancy Channels in the Conformal Bootstrap
Redundant operators motivate spectral gaps that block accidental symmetry enhancement, yielding the first bootstrap island for the 3D cubic CFT that excludes the O(3) model.
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Conformal scalar field theory from Ising tricriticality on the fuzzy sphere
A bilayer quantum Hall fuzzy-sphere model, tuned to an Ising tricritical point, realizes the conformally coupled free scalar CFT, verified by matching spectra, operator content, and bosonic algebra.
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On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions
The d→2 Wilson-Fisher limit is proposed to be strictly larger than the 2d Ising CFT, which emerges as a unitary subsector after negative-multiplicity operators cancel exactly.
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