Moduli Spaces of String Vacua with Four Supersymmetries

该奖项资助杜克大学罗宁·普莱瑟教授的研究活动。弦理论是引力量子理论和宇宙基本结构统一描述的主要竞争者。在过去的三十年里，弦理论的研究在物理和数学领域带来了令人兴奋的新见解。考虑弦在非平凡背景中的传播，产生了对时空中数学结构的物理解释。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，镜像对称是两个不同空间之间的一种令人惊讶的关系，当用作弦背景时，这种关系导致了错综复杂的物理。Plesser的研究将在这些结果和这两个领域的最新进展的基础上，在新的制度下继续进行这些研究。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。因此，这一领域的研究通过促进科学在一个特别跨学科的方向上的进步来促进国家利益。Plesser还将培训研究生，并让本科生参与研究。Plesser还将与当地公立学校合作，通过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，并激发年轻人对科学的热情。这些课程材料被广泛提供，供其他地方使用。此外，Plesser在过去十年中进行的定期公众观星活动将得到加强，包括天文摄影能力。更严格地说，Plesser将采用各种方法来更好地了解具有四个不间断超对称的弦真空的模空间结构。这包括微扰杂化真空和与之相关的(0，2)超共形场理论，以及关于Calabi-Yau四重结构的F理论和M理论紧化。这些公式中的每一个都给出了模空间的一个区域的简单描述，并且这两个描述在重叠区域中的关系是特别有趣的。

This award funds the research activities of Professor Ronen Plesser of Duke University.String theory is the leading contender for a quantum theory of gravity and a unified description of the fundamental structure of the universe. 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, a surprising relation between two distinct spaces that lead to indentical physics when used as string backgrounds. Plesser's research will build on these results and on recent progress in both fields to pursue these studies in new regimes. This work will be done in collaboration with physicists and mathematicians around the world, enhancing interdisciplinary cooperation. As a result, research in this area advances the national interest by promoting the progress of science in a particularly interdisciplinary direction. Plesser will also train graduate students and involve undergraduate students in the research. Plesser will also collaborate with local public schools to enhance science teaching and generate enthusiasm for science in young people through visits to the classroom to present specific curriculum materials developed in concert with the schools. These curriculum materials are made broadly available for use elsewhere. Moreover, the regular public stargazing events conducted by Plesser for the past decade will be enhanced by including astrophotography capabilities.More technically, Plesser will pursue various approaches to better understand the structure of the moduli space of string vacua with four unbroken supersymmetries. This includes perturbative heterotic vacua and the (0,2) superconformal field theories associated to these, as well as F-theory and M-theory compactifications on Calabi-Yau fourfolds. Each of these formulations gives a simple description of a region of the moduli space, and the relation between the two descriptions in regions of overlap is of particular interest.