超条带代数与费米子理论中的非微扰谱
Superstrip Algebras and Nonperturbative Spectra in Fermionic Theories
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中文总结 AI 辅助
本文构建费米子系统的超条带代数，应用于超共形极小模型的带隙红外相，计算Witten指标并揭示孤子携带分数费米子数，同时建立边界SymTFT框架。
中文摘要 AI 辅助
本文是arXiv:2511.22129的扩展版本。我们为具有费米子超融合范畴$\mathscr C$且真空结构由超模范畴$\mathcal M$描述的带隙(1+1)维系统，发展了超条带代数$\mathbf{sStr}_{\mathscr C}(\mathcal M)$的一般构造，该代数是对应于条带代数的费米子版本。作为示例，我们为两个简单例子具体计算了超条带代数：斐波那契融合范畴的费米子变体和q型$\mathbb{Z}_2$对称性。随后，我们将该框架应用于由最相关算符微扰的$\mathcal N=2$和$\mathcal N=1$超共形极小模型的带隙红外相，并计算了Witten指标。我们解释了粒子和孤子谱及其费米子宇称如何组织成相应超条带代数的表示。自发破缺对称性与未破缺费米子宇称$(-1)^F$之间的混合't Hooft反常进一步迫使每个$\mathcal N=2$孤子携带分数费米子数。最后，我们为费米子系统建立了边界SymTFT，并在本文研究的几个示例中重现了结果。
英文摘要
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.
发表机构
- Xiamen University（厦门大学）
- Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China（合肥基本理论彭桓武中心）
- Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）
- Korea Institute for Advanced Study（韩国高等科学院）
机构由 AI 辅助整理，请以论文原文为准。
