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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.08107 |
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| _version_ | 1866909517662388224 |
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| author | Gao, Zhi-Qiang Wu, Congjun |
| author_facet | Gao, Zhi-Qiang Wu, Congjun |
| contents | We construct a (1+1)-dimension continuum model of 4-component fermions incorporating the exceptional Lie group symmetry $G_2$. Four gapped and five gapless phases are identified via the one-loop renormalization group analysis. The gapped phases are controlled by four different stable $SO(8)$ Gross-Neveu fixed points, among which three exhibit an emergent triality, while the rest one possesses the self-triality, i.e., invariant under the triality mapping. The gapless phases include three $SO(7)$ critical ones, a $G_2$ critical one, and a Luttinger liquid. Three $SO(7)$ critical phases correspond to different $SO(7)$ Gross-Neveu fixed points connected by the triality relation similar to the gapped SO(8) case. The $G_2$ critical phase is controlled by an unstable fixed point described by a direct product of the Ising and tricritical Ising conformal field theories with the central charges $c=\frac{1}{2}$ and $c=\frac{7}{10}$, respectively, while the latter one is known to possess spacetime supersymmetry. In the lattice realization with a Hubbard-type interaction, the triality is broken into the duality between two $SO(7)$ symmetries and the supersymmetric $G_2$ critical phase exhibits the degeneracy between bosonic and fermionic states, which are reminiscences of the continuum model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08107 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From $G_2$ to $SO(8)$: Emergence and reminiscence of supersymmetry and triality Gao, Zhi-Qiang Wu, Congjun Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics We construct a (1+1)-dimension continuum model of 4-component fermions incorporating the exceptional Lie group symmetry $G_2$. Four gapped and five gapless phases are identified via the one-loop renormalization group analysis. The gapped phases are controlled by four different stable $SO(8)$ Gross-Neveu fixed points, among which three exhibit an emergent triality, while the rest one possesses the self-triality, i.e., invariant under the triality mapping. The gapless phases include three $SO(7)$ critical ones, a $G_2$ critical one, and a Luttinger liquid. Three $SO(7)$ critical phases correspond to different $SO(7)$ Gross-Neveu fixed points connected by the triality relation similar to the gapped SO(8) case. The $G_2$ critical phase is controlled by an unstable fixed point described by a direct product of the Ising and tricritical Ising conformal field theories with the central charges $c=\frac{1}{2}$ and $c=\frac{7}{10}$, respectively, while the latter one is known to possess spacetime supersymmetry. In the lattice realization with a Hubbard-type interaction, the triality is broken into the duality between two $SO(7)$ symmetries and the supersymmetric $G_2$ critical phase exhibits the degeneracy between bosonic and fermionic states, which are reminiscences of the continuum model. |
| title | From $G_2$ to $SO(8)$: Emergence and reminiscence of supersymmetry and triality |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2411.08107 |