论文标题
具有基于球形融合类别缺陷的状态总和模型
State sum models with defects based on spherical fusion categories
论文作者
论文摘要
我们定义了带有表面，线和点缺陷的三角剖分三角形的Turaev-Viro-Barrett-Westbury状态总和模型。表面缺陷是定向嵌入的2D PL子延伸物，并在带有双模块迹线的球形融合类别上标记为Bimodule类别。线和点缺陷在这些表面上形成了定向图，并用双模块函子和双模块自然变换标记。状态总和基于概括的6J符号，该符号编码缺陷数据的相干同构。我们证明了状态总和的三角剖分独立性，并表明它可以根据多边形图来计算，以满足定向表面的多边形表现的切割和粘合身份。通过计算缺陷表面的状态总和，我们表明它们检测到缺陷表面的属，并且对其嵌入敏感。我们表明，缺陷数据的缺陷表面上的缺陷线定义了基础球形融合类别中心的功能区不变。
We define a Turaev-Viro-Barrett-Westbury state sum model of triangulated 3-manifolds with surface, line and point defects. Surface defects are oriented embedded 2d PL submanifolds and are labeled with bimodule categories over spherical fusion categories with bimodule traces. Line and point defects form directed graphs on these surfaces and labeled with bimodule functors and bimodule natural transformations. The state sum is based on generalised 6j symbols that encode the coherence isomorphisms of the defect data. We prove the triangulation independence of the state sum and show that it can be computed in terms of polygon diagrams that satisfy the cutting and gluing identities for polygon presentations of oriented surfaces. By computing state sums with defect surfaces, we show that they detect the genus of a defect surface and are sensitive to its embedding. We show that defect lines on defect surfaces with trivial defect data define ribbon invariants for the centre of the underlying spherical fusion category.
