Aspects of Global String Compactifications

弦理论作为量子引力理论的主要候选者，既包括量子力学，也包括爱因斯坦的广义相对论。剩下的挑战是确定与我们的宇宙形成相关的一组适当的背景条件。压缩11维M理论/超重力可以产生非常大量的四维真空。因此，有必要理解这些额外的、紧凑的维度，并发现这些空间的性质与我们在宇宙中观察到的物理之间的联系。这项研究解决了字符串压缩的两个重要方面。一个主要的焦点是确定在全球磁通紧凑的背景下，呈现标准模型光谱的弦真空是如何存在的。这项研究还将应用宇宙学的约束条件，如宇宙微波背景，对从弦理论获得的膨胀型势施加限制。此外，还将讨论有关几何体细节的问题，如镜像对称性。第二种方法将研究AdS4/CFT3的各种特征，旨在提高我们对四维弦景观以及三维凝聚态系统的理解。这些项目加在一起是非常及时的，因为在接下来的几年里，来自欧洲核子研究中心大型强子对撞机(LHC)的数据将改善我们对标准模型以外的物理学的理解。此外，使用欧洲航天局普朗克卫星对宇宙微波背景进行更准确的观测，将为弦理论中可能出现的暴涨情景提供更严格的约束。更广泛的影响：拟议工作的结果将引起数学和物理界几个部门的兴趣。此外，拟议的活动将促进联合国大学物理和数学界以及地区、国家和国际合作科学家之间的合作和智力交流。此外，研究计划将与一个强有力的推广计划相结合，将粒子物理的前沿带入当地的高中。这将利用Theorynet以及UNH的现有基础设施，Theorynet是NSF在大波士顿地区赞助的项目，用于与高中教师和学生互动。这种互动将包括在PI在当地高中的演讲期间与教师和学生举行研讨会和非正式问答环节，以及高中访问北卡罗来纳大学以了解理论粒子物理的研究。

String theory, as a leading candidate for a quantum theory of gravity, encompasses both quantum mechanics and Einstein's theory of general relativity. A remaining challenge is the identification of the appropriate set of background conditions relevant to the formation of our universe. Compactifying the eleven-dimensional M-theory/supergravity can lead to a very large number of four dimensional vacua. It is therefore necessary to understand the extra, compact dimensions and discover the links between the properties of these spaces and the physics we observe in our universe. This research addresses two important aspects of string compactifications. A primary focus is the determination of how, in the context of global flux compactifications, string vacua exhibiting Standard Model like spectra exist. This study will also apply constraints from cosmology, such as the cosmic microwave background, to put restrictions on the inflationary type potentials obtained from string theory. In addition, questions regarding the details of the geometry, such as mirror symmetry, will be addressed. A second approach will be made in studying various features of AdS4/CFT3 aimed at improving our understanding of the four dimensional string landscape, as well as three dimensional condensed matter systems. The projects , taken together, are very timely since, during the course of the next few years, data from the Large Hadron Collider (LHC) at CERN will be improving our understanding of physics beyond the Standard Model. Furthermore, more accurate observations of the cosmic microwave background using the European Space Agency PLANCK satellite will provide even tighter constraints on the possible inflationary scenarios arising in string theory. Broader Impacts: Results from the proposed work will be of interest to several sectors of the mathematics and physics communities. Furthermore the proposed activities will foster collaborations and intellectual exchange within the UNH physics and mathematics community and amongst regional, national and international collaborating scientists. In addition the research program will be coupled with a strong outreach program taking the frontiers of particle physics into local high schools. This will capitalize on the existing infrastructure within the Theorynet, an NSF sponsored program in the greater Boston area, as well as at UNH, for interactions with high school teachers and students. Such interactions will include seminars and informal question-answer sessions with both teachers and students during presentations by the PI at local high schools, as well as visits by high schools to UNH to learn about research in theoretical particle physics.