论文标题
部分可观测时空混沌系统的无模型预测
Exploring Non-Invertible Symmetries in Free Theories
论文作者
论文摘要
对应于对应于使动作不变的基本领域的局部变换的对称性导致（可逆的）拓扑缺陷，这遵守了类似群体的融合规则。一个人可以通过从缺陷的一侧和另一侧的操作员之间指定规格不变的操作员之间的地图来构建更一般的拓扑缺陷。在这项工作中，我们将这种结构应用于麦克斯韦理论，并在四个维度上以及在二维中的自由紧凑型标量理论。就麦克斯韦理论而言，我们表明，将场强$ f $及其Hodge dual $ \ star f $混合的拓扑缺陷最多可以是$ so（2）$旋转。对于批量耦合的合理值和$θ$ - 角，我们找到了一个明确的缺陷Lagrangian，它实现了$ SO（2）$ Angle $φ$的值，因此$ \cosφ$也是合理的。我们进一步确定了此类缺陷对Wilson和'T Hooft Lines的作用，并表明它们通常是不可变的。我们在二维中重复对免费紧凑型标量$ ϕ $的分析。在这种情况下，我们只找到四个离散的地图：微不足道的地图，$ z_2 $ map $ dϕ \ rightarrow -dϕ $，$ \ mathcal {t} $ - 类似二元的映射$ dϕ \ rightArrow i \ rightarrow i \ star dϕ $，以及最后两个的产品。
Symmetries corresponding to local transformations of the fundamental fields that leave the action invariant give rise to (invertible) topological defects, which obey group-like fusion rules. One can construct more general (codimension-one) topological defects by specifying a map between gauge-invariant operators from one side of the defect and such operators on the other side. In this work, we apply such construction to Maxwell theory in four dimensions and to the free compact scalar theory in two dimensions. In the case of Maxwell theory, we show that a topological defect that mixes the field strength $F$ and its Hodge dual $\star F$ can be at most an $SO(2)$ rotation. For rational values of the bulk coupling and the $θ$-angle we find an explicit defect Lagrangian that realizes values of the $SO(2)$ angle $φ$ such that $\cos φ$ is also rational. We further determine the action of such defects on Wilson and 't Hooft lines and show that they are in general non-invertible. We repeat the analysis for the free compact scalar $ϕ$ in two dimensions. In this case we find only four discrete maps: the trivial one, a $Z_2$ map $dϕ\rightarrow -dϕ$, a $\mathcal{T}$-duality-like map $dϕ\rightarrow i \star dϕ$, and the product of the last two.
