Higher central charges and Witt groups
Higher central charges and Witt groups
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DOI：
10.1016/j.aim.2022.108388
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发表时间：
2020-02
影响因子：
1.7
通讯作者：
S. Ng;E. Rowell;Yilong Wang;Qing Zhang
中科院分区：
文献类型：
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作者：
S. Ng;E. Rowell;Yilong Wang;Qing Zhang
在本文中，我们介绍了编织融合类别的签名的定义，并证明了它们是其维特等价类的不变量。这些签名分配定义了威特群上的群同态。伪酉模范畴的较高中心电荷可以用这些签名来表示，这些签名被用来证明伊辛模范畴在维特群中对尖部取模具有无穷多个平方根。该结果进一步应用于证明Davydov-Nikshych-Ostrik关于超维特群的猜想：完全各向异性s-简单编织融合类别生成的挠子群具有无限秩。
In this paper, we introduce the definitions of signatures of braided fusion categories, which are proved to be invariants of their Witt equivalence classes. These signature assignments define group homomorphisms on the Witt group. The higher central charges of pseudounitary modular categories can be expressed in terms of these signatures, which are applied to prove that the Ising modular categories have infinitely many square roots in the Witt group modulo the pointed part. This result is further applied to prove a conjecture of Davydov-Nikshych-Ostrik on the super-Witt group: the torsion subgroup generated by the completely anisotropic s-simple braided fusion categories has infinite rank.