Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed "Platonic CFT". In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowed region in parameter space, which includes both the 3D (decoupled) Ising model and the Platonic CFT. The essential assumptions on the spectrum of operators used to provide the isolated allowed region include the existence of a stress-energy tensor and the irrelevance of certain operators (in the renormalization group sense).
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- 1 Stefanos R. Kousvos,
- 2 Andreas Stergiou
- CERN (through Organization: Organisation européenne pour la recherche nucléaire / European Organization for Nuclear Research [CERN])
- Hellenic Foundation for Research and Innovation [HFRI]
- Los Alamos National Laboratory [LANL]
- Mitsubishi International Corporation (through Organization: 三菱重工業株式会社 / Mitsubishi Heavy Industries (Japan) [MHI])
- Simons Foundation