Aspects of Global String Compactifications

弦理论作为引力量子理论的主要候选者，包含了量子力学和爱因斯坦的广义相对论。剩下的一个挑战是确定与我们宇宙形成有关的一组适当的背景条件。紧化11维M理论/超引力可以导致非常大量的四维真空。因此，有必要了解额外的紧凑维度，并发现这些空间的性质与我们在宇宙中观察到的物理学之间的联系。这项研究解决了字符串紧化的两个重要方面。一个主要的焦点是如何确定，在全球通量紧致化的背景下，弦真空展示标准模型的光谱存在。这项研究也将应用宇宙学的限制，如宇宙微波背景，把从弦理论得到的暴胀型潜力的限制。此外，关于几何细节的问题，如镜像对称，将得到解决。第二种方法将在研究各种功能的AdS 4/CFT 3旨在提高我们的理解的四维弦景观，以及三维凝聚态系统。这些项目合在一起非常及时，因为在未来几年内，来自欧洲核子研究中心大型强子对撞机（LHC）的数据将提高我们对标准模型之外的物理学的理解。此外，使用欧洲航天局普朗克卫星对宇宙微波背景辐射进行更精确的观测，将对弦论中可能出现的暴胀情景提供更严格的限制。更广泛的影响：拟议工作的结果将对数学和物理界的几个部门感兴趣。此外，拟议的活动将促进UNH物理和数学界以及区域、国家和国际合作科学家之间的合作和知识交流。此外，该研究计划将与一个强大的外展计划相结合，将粒子物理学的前沿带入当地高中。这将利用Theorynet内的现有基础设施，Theorynet是NSF在大波士顿地区以及UNH赞助的项目，用于与高中教师和学生进行互动。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会，以及高中访问UNH以了解理论粒子物理学研究。

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.