Face algebras and unitarity of SU(N)_L-TQFT

从非半单 TQFT 看 Burau 表示的稠密性与酉性

Density and unitarity of the Burau representation from a non-semisimple TQFT

本文利用四次单位根处的非半单 TQFT 构造 Burau 表示上的 Squier Hermitian 形式，并证明辫群在可能不定的酉表示空间中像稠密，同时探讨其拓扑量子计算应用。

Galois Orbits of TQFTs: Symmetries and Unitarity

We study Galois actions on $2+1$D topological quantum field theories (TQFTs), characterizing their interplay with theory factorization, gauging, the structure of gapped boundaries and dualities, 0-form symmetries, 1-form symmetries, and 2-groups. In order to gain a better physical understanding of Galois actions, we prove sufficient conditions for the preservation of unitarity. We then map out the Galois orbits of various classes of unitary TQFTs. The simplest such orbits are trivial (e.g., as in various theories of physical interest like the Toric Code, Double Semion, and 3-Fermion Model), an…

拓扑量子场论的自旋-统计定理

The spin-statistics theorem for topological quantum field theories

本文在Atiyah框架下通过引入费米子dagger紧致范畴，证明了拓扑量子场论的自旋-统计定理，并统一了自旋结构、超向量空间与幺正性。