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

We investigate the fate of 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 fermionic minimal model which possesses chiral $\mathbb{Z}_2$ symmetry (in addition number parity) and just relevant singlet operators, we can zero on four candidates. further least deformation leads supersymmetric (i.e. tricritical Ising model), rule out them matching spin contents preserved topological defect lines. The final candidates are $(11,4)$ if non-unitary, $(E_{6}, A_{10})$ unitary. If use constraint from double braiding relation proposed one authors, former scenario preferable.