局部F-理论模型的矩阵分解
Matrix Factorizations for Local F-Theory Models
摘要：
我用矩阵分解来描述膜在简单的奇点，因为它们出现在椭圆纤维的局部F-理论模型。ADE型奇点对应的Dynkin图的每个节点都与一个不可分解的矩阵分解相关联，该矩阵分解可以变形为一个或多个低秩的分解。具有内部通量的膜自然地作为不可分解因子分解的束缚态出现。以这种方式描述膜避免了解决奇点的需要，并编码了在传统F理论处理中被忽略的信息。本文的目的是展示如何膜产生的局部F-理论模型周围的简单奇点可以在这个框架中描述。
英文摘要：
I use matrix factorizations to describe branes at simple singularities as they appear in elliptic fibrations of local F-theory models. Each node of the corresponding Dynkin diagrams of the ADE-type singularities is associated with one indecomposable matrix factorization which can be deformed into one or more factorizations of lower rank. Branes with internal fluxes arise naturally as bound states of the indecomposable factorizations. Describing branes in such a way avoids the need to resolve singularities and encodes information which is neglected in conventional F-theory treatments. This paper aims to show how branes arising in local F-theory models around simple singularities can be described in this framework.
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