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

TL;DR

This paper explores the nature of a non-supersymmetric fixed point in two dimensions, identifying potential minimal models and using symmetry and topological defect line constraints to narrow down the candidates.

Contribution

It proposes a detailed analysis of the fixed point's possible minimal models, applying symmetry and defect line constraints to determine the most likely candidate.

Findings

Two main candidate models identified: fermionic (11,4) and (E6, A10) minimal models.

Using defect line matching, the non-unitary (11,4) model is less favored.

Additional constraints suggest the unitary (E6, A10) model as the more plausible fixed point.

Abstract

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 $\mathbb{Z}_2$ 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.