We initiate a systematic study of 2D gapped fermionic systems. When the system admits generalized symmetries that are spontaneously broken, we introduce an algebraic structure, dubbed the "superstrip algebra", to characterize the vacuum structure, particle/soliton degeneracies, and their quantum numbers in the far infra-red. As a demonstration, we apply this framework to the N=2 minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of SU(2)_k known to underlie the ADE classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting ADE-type soliton spectrum and their fractional fermion number. The talk is based on a recent work 2511.22129, collaborated with Zhihao Duan, Qiang Jia and Sungjay Lee.

Inviter: Jie-Qiang Wu