From G2 to SO(8): Emergence and reminiscence of supersymmetry and triality
Year: 2025
Type: article
Abstract: A bstract 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 = $$ \frac{1}{2} $$ 1 2 and c = $$ \frac{7}{10} $$ 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.
Source: Journal of High Energy Physics
Authors: Zhi-Qiang Gao, Congjun Wu
Institution: Westlake University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Awards: G1253933300, G8097029044
OpenAlex ID: W4408044537