Year: 2026
Type: preprint
Abstract: This is an extended version of arXiv:2511.22129. We develop a general construction of the superstrip algebra $\mathbf{sStr}_{\mathscr C}(\mathcal M)$, the fermionic counterpart of the strip algebra, for a gapped $(1+1)$-dimensional system with a fermionic superfusion category $\mathscr C$ and the vacuum structure described by the supermodule category $\mathcal M$. As illustrations, we work out the superstrip algebra for two simple examples: the fermionic variant of the Fibonacci fusion category and the q-type $\mathbb{Z}_2$ symmetry. We then apply the framework to the gapped IR phases of the $\mathcal N=2$ and $\mathcal N=1$ superconformal minimal models deformed by their least relevant operator and compute the Witten indices. We explain how the particle and soliton spectra, together with their fermion parity, are organized into representations of the corresponding superstrip algebras. A mixed 't Hooft anomaly between the spontaneously broken symmetry and the unbroken fermion parity $(-1)^F$ further forces each $\mathcal N =2$ soliton to carry a fractional fermion number. Finally, we set up the boundary SymTFT for fermionic systems and reproduce the results in several examples studied in this paper.
Source: arXiv (Cornell University)
Authors: Chen, Jin, Duan, Zhihao, Jia, Qiang, Lee, Sungjay
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, National Research Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, National Natural Science Foundation of China, Natural Science Foundation of Fujian Province, National Research Foundation of Korea, Korea Advanced Institute of Science and Technology
OpenAlex ID: W7212737004