标题： B膜传输和行列式簇的等级限制规则 显示英文标题

标题： B-brane Transport and Grade Restriction Rule for Determinantal Varieties

摘要： 我们研究与在$X$的弦论Kähler模空间中的环路的B-brane传输相关的$D^{b}Coh(X)$自等价。 我们考虑$X$为嵌入在$\mathbb{P}^{d}\times G(k,n)$中的某些行列式簇的解析的情况。 这类解析在一般情况下由非阿贝尔规范线性sigma模型(GLSM)进行建模。 我们使用GLSM构造，通过等级限制规则和半球分区函数的工具，确定与不同几何相之间B-brane传输相关的窗口范畴。 在分析的例子族中，围绕相边界的整体变换可以解释为链环补集内的环路。 我们利用这一解释将自等价分解为更简单的球形函子，并在两个由阿贝尔和非阿贝尔GLSM分别建模的卡拉比-丘3流形$X$的例子中进行了说明。 此外，我们还明确确定了自等价在格罗滕迪克群$K(X)$（或等价地，B-brane电荷）上的作用。 显示英文摘要

摘要： We study autoequivalences of $D^{b}Coh(X)$ associated to B-brane transport around loops in the stringy K\"ahler moduli of $X$. We consider the case of $X$ being certain resolutions of determinantal varieties embedded in $\mathbb{P}^{d}\times G(k,n)$. Such resolutions have been modeled, in general, by nonabelian gauged linear sigma models (GLSM). We use the GLSM construction to determine the window categories associated with B-brane transport between different geometric phases using the machinery of grade restriction rule and the hemisphere partition function. In the family of examples analyzed the monodromies around phase boundaries enjoy the interpretation as loop inside link complements. We exploit this interpretation to find a decomposition of autoequivalences into simpler spherical functors and we illustrate this in two examples of Calabi-Yau 3-folds $X$, modeled by an abelian and nonabelian GLSM respectively. In additon we also determine explicitly the action of the autoequivalences on the Grothendieck group $K(X)$ (or equivalently, B-brane charges).