Description
Anomaly matching for continuous symmetries has been the primary tool for establishing symmetry-enforced gaplessness. In this talk, I introduce a new mechanism based on symmetry spans: configurations in which a symmetry E is simultaneously embedded into two larger symmetries C and D. When the sets of gapped phases compatible with each embedding have no overlap, gaplessness is enforced.
In the first introductory part, I explain the classification of symmetric gapped phases as module categories and the restriction of symmetries as pullbacks of module categories. In the second part, I present the span criterion and explicit examples in 1+1d CFTs and lattice spin chains. Notably, this mechanism operates with discrete symmetries and continuous symmetries without anomalies, both of which admit well-understood lattice realizations. Based on joint work with Takamasa Ando [arXiv:2602.11696].
