A Mathematical Theory of the Gauged Linear Sigma Model
A Mathematical Theory of the Gauged Linear Sigma Model
复制标题
DOI：
10.2140/gt.2018.22.235
复制
发表时间：
2015-06
期刊：
影响因子：
--
通讯作者：
Huijun Fan;Tyler Jarvis;Y. Ruan
中科院分区：
文献类型：
--
作者：
Huijun Fan;Tyler Jarvis;Y. Ruan
我们构建了威滕测量线性西格玛模型（GLSM）的数学理论。我们的理论适用于广泛的例子，包括许多非阿贝尔规范群的情况。 Calabi-Yau 完全交集 X 的 Gromov-Witten 理论和 X 的 Landau-Ginzburg 对偶（FJRW 理论）都可以表示为计量线性 sigma 模型。此外，Landau-Ginzburg/Calabi-Yau 对应关系可以解释为 GLSM 中矩图的变化或 GIT 的变形。本文主要关注代数理论，而另一篇文章将讨论解析理论。
We construct a mathematical theory of Witten's Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with non-Abelian gauge group. Both the Gromov-Witten theory of a Calabi-Yau complete intersection X and the Landau-Ginzburg dual (FJRW-theory) of X can be expressed as gauged linear sigma models. Furthermore, the Landau-Ginzburg/Calabi-Yau correspondence can be interpreted as a variation of the moment map or a deformation of GIT in the GLSM. This paper focuses primarily on the algebraic theory, while a companion article will treat the analytic theory.