Abstract 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 ucsb gaucho blue 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 = 1 2 $$ rac{1}{2} $$ michael harris sunglasses and c = 7 10 $$ rac{7}{10} $$ , 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.