论文标题
FANO 3倍，反身多型和Brane Brick型号
Fano 3-Folds, Reflexive Polytopes and Brane Brick Models
论文作者
论文摘要
n个维度的反射性多面体在数学和理论物理学上引起了很多关注，因为它们与fano n折和镜像对称性的联系。这项工作着重于对应于光滑的3倍的18个常规反射型多面体。我们首次表明，所有18种常规反射性多面体都具有Brane Brick Models实现的相应2D（0,2）规格。这些2D量规的理论可被视为D1溴的世界情报理论，探测了曲曲面的calabi-yau 4 sistulinition，其圆环图由相关的常规反射性多面体给出。由于等级3中式风味对称性的电荷，因此显示出Brane Brick模型的中间模量空间的发电机形成发电机的晶格。结果表明，发电机的晶格是Brane Brick模型相应的曲折图的确切极性双反射多物。这种二元性不仅突出了几何学和2D仪理论之间的紧密关系，而且还为反思性多面体和勃雷砖模型开辟了通往新发现的途径。
Reflexive polytopes in n dimensions have attracted much attention both in mathematics and theoretical physics due to their connection to Fano n-folds and mirror symmetry. This work focuses on the 18 regular reflexive polytopes corresponding to smooth Fano 3-folds. For the first time, we show that all 18 regular reflexive polytopes have corresponding 2d (0,2) gauge theories realized by brane brick models. These 2d gauge theories can be considered as the worldvolume theories of D1-branes probing the toric Calabi-Yau 4-singularities whose toric diagrams are given by the associated regular reflexive polytopes. The generators of the mesonic moduli space of the brane brick models are shown to form a lattice of generators due to the charges under the rank 3 mesonic flavor symmetry. It is shown that the lattice of generators is the exact polar dual reflexive polytope to the corresponding toric diagram of the brane brick model. This duality not only highlights the close relationship between the geometry and 2d gauge theory, but also opens up pathways towards new discoveries in relation to reflexive polytopes and brane brick models.
