增强规范对称性与辫群作用量
Enhanced gauge symmetry and braid group actions
摘要：
加强规范对称性出现在II型弦理论（以及F-和M-理论）紧化的卡拉比-丘流形包含例外的因子会议在Dynkin配置。它表明，在许多这样的情况下，在增强的对称点的模量的辫群的行为上的导出范畴的各种层。这个辫群覆盖了增强对称代数的外尔群，它本身以兼容的方式作用于变种的变形空间。扩展这一结果给出了非平凡的$B$ -字段的K3表面上，解释物理限制的$B$ -字段，以及椭圆纤维。本文的观点也为局部$A_{2n}$组态在具有整体$\Z/2$单值性的三重组态中的规范对称性增强提供了新的证据。
英文摘要：
Enhanced gauge symmetry appears in Type II string theory (as well as F- and M-theory) compactified on Calabi--Yau manifolds containing exceptional divisors meeting in Dynkin configurations. It is shown that in many such cases, at enhanced symmetry points in moduli a braid group acts on the derived category of sheaves of the variety. This braid group covers the Weyl group of the enhanced symmetry algebra, which itself acts on the deformation space of the variety in a compatible fashion. Extensions of this result are given for nontrivial $B$-fields on K3 surfaces, explaining physical restrictions on the $B$-field, as well as for elliptic fibrations. The present point of view also gives new evidence for the enhanced gauge symmetry content in the case of a local $A_{2n}$-configuration in a threefold having global $\Z/2$ monodromy.
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