Logarithmic Gauged Linear Sigma Models

对数测量线性西格玛模型

基本信息

批准号：
2054830
负责人：
Felix Janda
金额：
$ 13.79万
依托单位：
University of Notre Dame
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2054830&HistoricalAwards=false
关键词：
Logarithmic Gauged Linear Sigma Models

项目摘要

Over the past few decades, deep connections between pure mathematics and physics have developed. One such area of fruitful interaction is between string theory, a branch of theoretical physics connected with the structure of elementary particles, and enumerative geometry, which studies counts of the number of solutions to geometric problems (how many lines, for example, pass through four fixed lines in space). This project will develop a new technique, which is inspired from the gauged linear sigma model (GLSM) in physics, to solve several enumerative problems.In more detail, the project will develop a new technique (log GLSM) in higher genus Gromov-Witten theory. The goal is to prove conjectures from physics such as the holomorphic anomaly equations for quintic threefolds and more general complete intersection Calabi-Yau 3-folds. For this, a new moduli space will be constructed whose localization formula gives a way of computing Gromov-Witten invariants of a convex complete intersection from those of its ambient space, and new "effective invariants". Different applications will exploit the structure of the localization formula, and correspondences between effective invariants.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在过去的几十年中，纯数学和物理学之间的深厚联系已经发展。富有成果的相互作用的一个领域是弦理论（与基本颗粒结构相关的理论物理学的一个分支和枚举的几何形状相关的一个分支，研究都研究了几何问题的解决方案数量（例如，有多少线经过太空中的四个固定线）。该项目将开发一种新技术，该技术的灵感来自物理学中的测量线性Sigma模型（GLSM），以解决几个枚举问题。从更详细的角度来看，该项目将在高级Gromov-witten理论中开发一种新技术（LOOD GLSM）。目的是证明来自物理学的猜想，例如五重五倍的骨膜异常方程，以及更一般的完整交点Calabi-yau 3倍。为此，将构建一个新的模量空间，其本地化公式提供了一种从其环境空间的凸面完整相交和新的“有效不变式”的完整交集的方法。不同的申请将利用本地化公式的结构，并在有效不变的情况下进行对应关系。该奖项反映了NSF的法定任务，并认为使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估。