Description
We discuss a family of non-invertible topological defects in two-dimensional theories of n Weyl fermions. The construction relies on the existence of G-symmetric conformal boundary conditions for nDirac fermions. Upon unfolding, these boundary conditions become topological defects D of n Weyl fermions that intertwine the two G-representations, and they are generically non-invertible. We illustrate this construction when G= U(1)^n, where the topological defect D can be shown to be a duality defect associated with gauging certain finite abelian group Γ. By contrast, for certain non-Abelian symmetry including the G= SU(2) symmetry appearing in the 1-5-7-8-9 problem, we prove that D cannot be realized as a duality defect for gauging any finite Abelian group. We explain how the duality-defect perspective can be used to re-derive the fermion scattering from a conformal boundary.