Superstrip Algebras and Nonperturbative Spectra in Fermionic Theories

Abstract

This is an extended version of arXiv:2511.22129. We develop a general construction of the superstrip algebra sStr_𝒞(ℳ), the fermionic counterpart of the strip algebra, for a gapped (1+1)-dimensional system with a fermionic superfusion category 𝒞 and the vacuum structure described by the supermodule category 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 ℤ₂ symmetry. We then apply the framework to the gapped IR phases of the 𝒩=2 and 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 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.

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BibTeX RIS

BibTeX

@misc{chen2026superstrip,
  title = {{Superstrip Algebras and Nonperturbative Spectra in Fermionic Theories}},
  author = {Jin Chen and Zhihao Duan and Qiang Jia and Sungjay Lee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12750},
  eprint = {2609.12750},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12750},
}

RIS

TY  - UNPB
TI  - Superstrip Algebras and Nonperturbative Spectra in Fermionic Theories
AU  - Jin Chen
AU  - Zhihao Duan
AU  - Qiang Jia
AU  - Sungjay Lee
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12750
UR  - https://arxiv.org/abs/2609.12750
AB  - This is an extended version of arXiv:2511.22129. We develop a general construction of the superstrip algebra sStr_𝒞(ℳ), the fermionic counterpart of the strip algebra, for a gapped (1+1)-dimensional system with a fermionic superfusion category 𝒞 and the vacuum structure described by the supermodule category 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 ℤ_2 symmetry. We then apply the framework to the gapped IR phases of the 𝒩=2 and 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 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.
ER  -

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