玻色子模型中的Angular momentum非守恒对称性

论 2+1 维中玻色与费米一形式对称性的分类及 't Hooft 反常匹配

On the Classification of Bosonic and Fermionic One-Form Symmetries in $2+1$d and 't Hooft Anomaly Matching

本文研究 2+1 维中由玻色和费米自统计拓扑线构成的 BFB 一形式对称性，论证其可分类且与群密切相关，并利用该分类研究具有 BFB 对称性的非拓扑 QFT 的重整化群流不变量。

Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy

In this paper, we construct the additional symmetries of the fermionic $(2N,2M)$-Toda hierarchy basing on the generalization of the $N{=}(1|1)$ supersymmetric two dimensional Toda lattice hierarchy. These additional flows constitute a $w_{\infty}\times w_{\infty}$ Lie algebra. As a Bosonic reduction of the $N{=}(1|1)$ supersymmetric two dimensional Toda lattice hierarchy and the fermionic $(2N,2M)$-Toda hierarchy, we define a new extended fermionic $(2N,2M)$-Toda hierarchy which admits a Bosonic Block type superconformal structure.

玻色单例的显共形描述和高阶对称性

Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons

通常的共形场的环境空间方法是基于将d维共形空间识别为平坦d+2维环境空间中的狄拉克投影超锥。在这项工作中，我们明确地集中在任何整数自旋的单态，并提出了一种方法，允许一个有地方性和共形对称性的表现。这是通过在光纤中而不是在时空中使用环境空间表示来实现的。这种方法使我们能够刻画任意玻色子单粒子的高阶对称子代数，它是反德西特时空上混合对称规范场的候选高阶自旋代数。此外，我们认为，这个代数实际上用尽所有更高的对称性。

Virasoro Algebra and Asymptotic Symmetries from Fractional Bosonic Strings

The aim of this work is to further study the fractional bosonic string theory. In particular, we wrote the energy-momentum tensor in the fractional conformal gauge and study their symmetries. We introduced the Virasoro operators of all orders. In fact, we found the same $L_0 (\widetilde{L}_0)$ operator originally defined in the work of fractional bosonic string up to a shift transformation. Also, we compute the algebra of our Fractional Virasoro Operators, finding that the satifies the $Witt$ algebra. Lastly, we showed that in the boundary of our theory we recover the lost conservation law ass…

Extended real Clifford-Dirac algebra and bosonic symmetries of the Dirac equation with nonzero mass

Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional gamma matrix representations of the Clifford algebra and corresponding representations of SO(10) and SO(1,9) algebras over the field of real numbers are introduced. This turned out to be possible in the space of eight-component spinors, and not for the ordinary four-component Dirac spinors. The proposed mathematical objects allow the generalization of our resu…

Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries

Gapped quantum liquids (GQL) include both topologically ordered states (with long range entanglement) and symmetry protected topological (SPT) states (with short range entanglement). In this paper, we propose a classification of 2+1D GQL for both bosonic and fermionic systems: 2+1D bosonic/fermionic GQLs with finite on-site symmetry are classified by non-degenerate unitary braided fusion categories over a symmetric fusion category (SFC) $\cal E$, abbreviated as $\text{UMTC}_{/\cal E}$, together with their modular extensions and total chiral central charges. The SFC $\cal E$ is $\text{Rep}(G)$ …