The fate of non-supersymmetric Gross-Neveu-Yukawa fixed point in two dimensions

We investigate the fate of the non-supersymmetric Gross-Neveu-Yukawa fixed point found by Fei et al. in 4 - epsilon dimensions with a two-component Majorana fermion continued to two dimensions. Assuming that it is a fermionic minimal model which possesses a chiral DOUBLE-STRUCK CAPITAL Z(2) symmetry (in addition to fermion number parity) and just two relevant singlet operators, we can zero in on four candidates. Assuming further that the least relevant deformation leads to the supersymmetric Gross-Neveu-Yukawa fixed point (i.e. fermionic tricritical Ising model), we can rule out two of them by matching the spin contents of the preserved topological defect lines. The final candidates are the fermionic (11, 4) minimal model if it is non-unitary, and the fermionic (E-6, A(10)) minimal model if it is unitary. If we further use a constraint from the double braiding relation proposed by one of the authors, the former scenario is preferable.

Automated summary

In this study, the fate of the non-supersymmetric Gross-Neveu-Yukawa fixed point in 4 - epsilon dimensions with a two-component Majorana fermion continued to two dimensions is investigated. Assuming it is a fermionic minimal model with a chiral DOUBLE-STRUCK CAPITAL Z(2) symmetry and two relevant singlet operators, four candidates are narrowed down. By matching the spin contents of the preserved topological defect lines and using a constraint from the double braiding relation, the preferred scenario is determined to be either the fermionic (11, 4) minimal model if it is non-unitary, or the fermionic (E-6, A(10)) minimal model if it is unitary.