Geometry and Physics of String Compactifications

在过去的三十年里，弦理论的研究在物理学和数学方面带来了令人兴奋的新见解。考虑弦在非平凡背景下的传播，为时空中的数学结构提供了物理解释。数学和物理直觉和技术之间的相互作用丰富了这两个领域。一个值得注意的例子是镜像对称的发现和许多应用。本文所述的研究将以这些结果和这两个领域的最新进展为基础，在新的体制下进行这些研究。目的之一是利用各种方法提高我们对异质弦紧化的几何和物理的理解。这些模型可以描述类似于我们的宇宙，具有非阿贝尔规范对称性和手性物质含量等特征。此外，利用几何学和场论的见解对m理论紧化中的极值跃迁进行研究，以了解可能的动力学。这项工作有望使人们更好地理解弦理论的物理学，并深入了解CalabiYau空间的数学。更广泛的影响：这项工作将与世界各地的物理学家和数学家合作完成，加强跨学科合作。经验表明，这一领域的这种合作是富有成效的，因为新的物理见解和纯数学的新结果齐头并进。PI还将培训研究生，并让本科生参与研究。他也将加强他的外展活动计划。这包括与当地公立学校合作，通过PI和/或PI培训的学生访问教室，展示与学校合作开发的具体课程材料，加强科学教学，激发年轻人对科学的热情。这些课程材料广泛地提供给其他地方使用。PI在过去十年中定期进行的公众观星活动将通过包括天体摄影功能而得到加强。

Research in string theory in the past three decades has led to exciting new insights in physics and mathematics. Considering string propagation in nontrivial backgrounds produces physical interpretations for mathematical structures in spacetime. The interplay between mathematical and physical intuitions and techniques has enriched both fields. A notable example of this is the discovery and the many applications of mirror symmetry. The research described here will build on these results and on recent progress in both fields to pursue these studies in new regimes. One aim is to improve our understanding of the geometry and physics of heterotic string compactifications using a variety of approaches. These models can describe universes similar to ours with such features as nonabelian gauge symmetry and chiral matter content. In addition an investigation of extremal transitions in M-theory compactifications using insights from geometry and field theory will be carried out to learn about the possible dynamics. This work is expected to lead to a better understanding of the physics of string theory, as well as to insight into the mathematics of CalabiYau spaces. Broader Impact: This work will be done in collaboration with physicists and mathematicians around the world, enhancing interdisciplinary cooperation. Experience shows that such collaborations in this field have been productive , as new physics insights and new results in pure mathematics go hand-in-hand. The PI will also train graduate students and involve undergraduate students in the research. He will also enhance his program of outreach activities. This includes collaborations with local public schools to enhance science teaching and generate enthusiasm for science in young people by visits to the classroom by the PI and/or by students trained by the PI to present specific curriculum materials developed in concert with the schools. These curriculum materials are made broadly available for use elsewhere. The regular public stargazing events conducted by the PI for the past decade will be enhanced by including astrophotography capabilities.