arXiv 1609.017232016-09-06hep-thmath-phmath.AGmath.MP

镜子中的Brane Brick模型

Brane Brick Models in the Mirror

Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong, Cumrun Vafa

备注：: 74 pages, 56 figures
发表信息：: JHEP 1702:106,2017
DOI：: 10.1007/JHEP02(2017)106

摘要：

膜砖模型是IIA型膜结构，它编码了D1-膜世界体积上的$2d$ $\mathcal{N}=(0,2)$规范理论，探测复曲面的卡-丘4-折叠。我们使用镜像对称，以提高我们的理解，这种对应关系，并提供了一个系统的方法，从几何开始构建膜砖模型。镜像组态由D5-膜包裹4-球组成，规范理论由它们如何相交决定。我们还解释了如何$2d$ $(0,2)$ triality实现的几何过渡的镜子几何。镜像对称导致了不同维度上对偶的几何统一，其中对偶的阶数为$n-1$（对于卡-丘$n$ -折叠）。这使我们猜想在$0d$中存在一个四次对称。最后，我们评论如何M-理论提升膜砖模型连接到分类的$2d$ $(0,2)$理论的4-流形。

英文摘要：

Brane brick models are Type IIA brane configurations that encode the $2d$ $\mathcal{N}=(0,2)$ gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror configuration consists of D5-branes wrapping 4-spheres and the gauge theory is determined by how they intersect. We also explain how $2d$ $(0,2)$ triality is realized in terms of geometric transitions in the mirror geometry. Mirror symmetry leads to a geometric unification of dualities in different dimensions, where the order of duality is $n-1$ for a Calabi-Yau $n$-fold. This makes us conjecture the existence of a quadrality symmetry in $0d$. Finally, we comment on how the M-theory lift of brane brick models connects to the classification of $2d$ $(0,2)$ theories in terms of 4-manifolds.

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摘要：

英文摘要：

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