In some quantum theories, symmetries intertwine in an unusual way, as if a lock had two keys, but turning one slightly shifted the other. Such intertwined symmetries are called 2-groups. One is an ordinary symmetry acting on point particles (0-form), and the other is a 'linear' symmetry (1-form) governing extended objects like strings or lines.

The authors considered lines charged under the 1-form symmetry and found that they necessarily break the 0-form symmetry. This is not a flaw of the model but a topological obstruction — a 'family anomaly' that persists under any renormalization group flow. The breaking generates a whole family of lines, parametrized by the broken symmetry generators.

For the analysis, they used the Wess–Zumino consistency condition and a generalized anomaly inflow formalism. In the non-Abelian case, the anomaly arises from a higher Berry connection on the moduli space of defects. In the Abelian case, they applied differential cohomology; in the discrete case, they reformulated it via the associativity of symmetry defects.

The work clarifies how line symmetry breaking relates to the hierarchy of breakings in the bulk and points to subtle differences between simple and non-simple lines. All of this constitutes universal constraints independent of the specific model.