格贝斯，协变导数，p型格点规范理论，杨-巴克斯特方程
Gerbes, covariant derivatives, p-form lattice gauge theory, and the Yang-Baxter equation
摘要：
在p型格点规范理论中，涨落变量存在于p维格胞上，并围绕（p+1）维格胞相互作用。有人认为，该模型的连续统版本应该由（p-1）-gerbes描述。然而，只理解gerbes的连接和曲率，而不是协变导数。利用格点类比，提出了格贝的另一种定义：截面是函数phi（x，s），其中x是基点，s是表面元素。在这个纯粹的局部形式主义中，存在一个自然的协变导数。杨-巴克斯特方程，以及更一般的单纯形方程，都是零曲率条件。描述了向量场代数和格贝规范变换的作用，以及它们的阿贝尔扩张。
英文摘要：
In p-form lattice gauge theory, the fluctuating variables live on p-dimensional cells and interact around (p+1)-dimensional cells. It has been argued that the continuum version of this model should be described by (p-1)-gerbes. However, only connections and curvatures for gerbes are understood, not covariant derivatives. Using the lattice analogy, an alternative definition of gerbes is proposed: sections are functions phi(x,s), were x is the base point and s is the surface element. In this purely local formalism, there is a natural covariant derivative. The Yang-Baxter equation, and more generally the simplex equations, arise as zero-curvature conditions. The action of algebras of vector fields and gerbe gauge transformations, and their abelian extensions, are described.
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