Research in string compactifications and mathematical string theory

PI建议研究由弦理论的紧化得到的具有N=1超对称性的四维理论的性质。另一个研究的主题是几何和弦理论之间的联系。另一个目标将是研究“镜像对称”的特殊推广，镜像对称是典型的不同拓扑空间之间的二元性。PI还希望研究具有通量的杂交弦紧凑化，这涉及到理解不属于通常的卡勒变种的流形。这项研究的其他方向包括研究一类源自兰道-金兹堡模型的弦真空。这一提议的更广泛影响是，PI提议为来访的研究生和博士后开设一系列为期两周的强化暑期班，向年轻物理学家教授相关的高等数学。这一系列暑期班将有助于填补在这一领域对年轻人的培训方面的重大教学空白，即缺乏学校教授在正规弦论方面取得进展所需的高等数学。这项建议中所提倡的研究是多学科性质的，涉及与具有几何专业知识的数学家合作。

The PI proposes to investigate the properties of four dimensional theories with N = 1 supersymmetry which are obtained from compactifications of string theory. Another topic of investigation will be the connection between geometry and string theory. Another objective will be to study a particular generalization of "mirror symmetry," a duality between typically topologically distinct spaces. The PI also hopes to study heterotic string compactifications with fluxes which involve understanding manifolds that are not of the usual Kahler variety. Other directions of this research include studying a class of string vacua derived from "hybrid" Landau-Ginzburg models.The broader impacts of this proposal are that the PI proposes a series of intensive two-week summer schools for visiting grad students and postdocs to teach relevant advanced mathematics to young physicists. This series of summer schools will help to fill what the PI perceives as a significant pedagogical gap in the training of young persons in this field namely the lack of schools to teach the advanced mathematics needed to make progress in formal string theory. The research advocated in this proposal is multidisciplinary in nature involving collaboration with mathematicians with expertise in geometry