Foundations of F-Theory

弦理论提供了粒子物理理论模型的一致高能外推，并自然地将这些模型与引力统一起来，并为数学物理提供了工具，在理论物理中有许多应用。一种被称为F理论的有前途的弦理论模型近年来重新引起人们的兴趣，这表明了一些基础研究的必要性。这些研究涉及一个复杂的数学分支--代数几何，它为构建物理模型提供了背景。PI将决定对F理论模型的规范群和物质含量的限制是什么，对于Calabi-Yau三重和Calabi-Yau四重；是否每个椭圆纤维的Calabi-Yau四重都是等维族的二次元，如果不是，大维度纤维的物理解释是什么；椭圆纤维的Calabi-Yau流形的基的结构；Calabi-Yau流形的F理论解释具有不是椭圆的亏格一纤维(即，没有截面)；四重椭圆纤维Calabi-Yau全空间的二元几何如何与这四重上的通量选择相互作用，特别是F-理论真空必然被通量提升到什么程度；T-膜理论的M-理论双重解释；F-理论和非几何杂化弦之间的对偶性能否被推广；以及Calabi-Yau几何中可能与F-理论相关的其他主题，包括进一步探索最近发现的描述Calabi-Yau流形的规范线性西格玛模型通过S2上的配分函数包含关于Calabi-Yau流形的大量信息。更广泛的影响该项目还将通过国际和平研究所在本科生、研究生和博士后各级的教育活动，以及通过国际和平研究所不断努力简化科学交流，使尽可能多的科学信息以电子方式提供，从而产生更广泛的影响。

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.