arXiv 2402.069932024-02-10hep-th

来自 Branes 的 2d (0,2) 规范理论：Brane Brick Models 的近期进展

2d (0,2) Gauge Theories from Branes: Recent Progress in Brane Brick Models

Sebastián Franco

备注：: 12 pages, 9 figures

AI总结：

本文回顾了 Brane Brick Models 在实现 $2d$ $(0,2)$ 规范理论中的进展，介绍了高效生成模型的方法，并构建了所有光滑 Fano 3-folds 锥及两族 Sasaki-Einstein 7-manifolds 的规范理论。

摘要：

我们讨论了利用 branes 实现 $2d$ $(0,2)$ 规范理论，重点研究 Brane Brick Models，它们与探测环面 Calabi-Yau 4-folds 的 D1-branes 是 T-dual 的。这些 brane 设置完整编码了 D1-branes 世界体积上无限类别的 $2d$ $(0,2)$ quiver 规范理论，并极大简化了它们与被探测几何之间的联系。我们回顾了高效生成 Brane Brick Models 的多种方法。随后，这些算法被用于构建所有光滑 Fano 3-folds 上的锥以及两族已知度量的无限 Sasaki-Einstein 7-manifolds 的 $2d$ $(0,2)$ 规范理论。本文基于作者在 Simons Center for Geometry and Physics 举行的 Gauged Linear Sigma Models @ 30 会议上的报告。

英文摘要：

We discuss the realization of $2d$ $(0,2)$ gauge theories in terms of branes focusing on Brane Brick Models, which are T-dual to D1-branes probing toric Calabi-Yau 4-folds. These brane setups fully encode the infinite class of $2d$ $(0,2)$ quiver gauge theories on the worldvolume of the D1-branes and substantially streamline their connection to the probed geometries. We review various methods for efficiently generating Brane Brick Models. These algorithms are then used to construct $2d$ $(0,2)$ gauge theories for the cones over all the smooth Fano 3-folds and two infinite families of Sasaki-Einstein 7-manifolds with known metrics. This note is based on the author's talk at the Gauged Linear Sigma Models @ 30 conference at the Simons Center for Geometry and Physics.

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