Foundations of F-Theory

F 理论基础

• 批准号: 1307513
• 负责人: David Morrison
• 金额: $ 35.4万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-10-01 至 2017-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1307513&HistoricalAwards=false
• 关键词: Foundations; Theory

String theory provides consistent high-energy extrapolations of theoretical models of particle physics, as well as naturally unifying those models with gravity, and provides tools of mathematical physics with a number of applications in theoretical physics. One promising type of string theory model known as F-theory has seen a resurgence of interest in recent years which points out the need for some basic foundational studies. These studies involve a sophisticated branch of mathematics, algebraic geometry, which provides the background for constructing the physical models. The PI will determine what are the restrictions for gauge groups and matter content for F-theory models, both on Calabi-Yau threefolds and Calabi-Yau fourfolds; whether every elliptically-fibered Calabi-Yau fourfold is birational to an equidimensional family, and if not, what is the physical interpretation of the fibers of large dimension; the structure of the base of an elliptically fibered Calabi-Yau manifold; the F-theory interpretation of Calabi-Yau manifolds which have a genus one fibration that is not elliptic (i.e., there is no section); how the birational geometry of the total space of an elliptically fibered Calabi-Yau fourfold interacts with the choices of flux on that fourfold, and in particular, to what extent F-theory vacua are necessarily lifted by fluxes; the M-theory dual interpretation of the theory of T-branes; can the duality between F-theory and nongeometric heterotic strings be extended; and other topics in Calabi-Yau geometry which may be relevant to F-theory, including further exploration of the recent discovery that the gauged linear sigma models which describe Calabi-Yau manifolds contain via a partition function on S2 a wealth of information about the Calabi-Yau manifold. Broader Impact The project will also have a broader impact through educational activities of the PI, at the undergraduate, graduate and postdoctoral levels, as well as through the PI's ongoing efforts to streamline scientific communication by making as much of it available electronically as possible.

弦理论提供了粒子物理学理论模型的一致高能外推，以及自然地将这些模型与引力统一起来，并提供了数学物理学的工具，在理论物理学中有许多应用。近年来，一种被称为F理论的有前途的弦理论模型重新引起了人们的兴趣，这表明需要进行一些基本的基础研究。这些研究涉及到数学的一个复杂的分支--代数几何，它为构造物理模型提供了背景。PI将确定F理论模型（无论是卡-丘三重模型还是卡-丘四重模型）的规范群和物质含量的限制;每个椭圆纤维卡-丘四重模型是否对于等维族是双有理的，如果不是，什么是大维度纤维的物理解释;椭圆纤维卡-丘流形的基底结构;具有非椭圆亏格的纤维化的Calabi-Yau流形的F-理论解释（即，没有章节）;椭圆纤维卡-丘四重体的全空间的双有理几何如何与四重体上通量的选择相互作用，特别是，通量在多大程度上必然提升F-理论真空; T-膜理论的M-理论对偶解释; F-理论和非几何杂化弦之间的对偶性是否可以扩展;以及其他可能与F理论相关的卡-丘几何主题，包括进一步探索最近发现的描述卡-丘流形的规范线性sigma模型通过S2上的配分函数包含关于卡-丘流形的丰富信息。该项目还将通过PI在本科生、研究生和博士后层面的教育活动以及PI通过尽可能多地以电子方式提供科学交流来简化科学交流的持续努力产生更广泛的影响。