Translation invariant defects as an extension of topological symmetries

The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings, we focus on line defects in 2dQFT and we point out that topological defects naturally embed into a larger class, namely, translation invariant defects. The latter still allow for nonsingular fusion and one obtains a monoidal category of translation invariant defects which contains that of topological defects as a full subcategory. We give a simple perturbative description of translation invariant defects in a perturbed conformal field theory via chiral three-dimensional topological field theory. We show in the example of the Ising CFT and the Lee–Yang CFT that even if no topological defects survive the deformation, some translation invariant defects still do.