Geometry of Strings and Gravity

弦与重力的几何

• 批准号: 0937443
• 负责人: Shing-Tung Yau
• 金额: $ 39.17万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0937443&HistoricalAwards=false
• 关键词: Geometry; Strings; Gravity

Problems of fundamental physics in the context of string theory and gravity can often be rephrased purely as problems in geometry, the space of vacua of string theory and in particular the spectrum of supersymmetric (BPS) objects on them. On certain "walls" in the moduli space of vacua, a BPS object can decay to less massive BPS objects. Such a wallcrossing phenomenon has an extremely rich and mysterious mathematical structure. It is proposed to study wall-crossings from various points of views including vacua with high number of supersymmetries, applying tools of mirror symmetry and string dualities. Understanding the spectrum of BPS objects is important for calculating black hole entropy and topological string theory. The PI proposes to uncover new geometrical invariants which are necessary for physically characterizing these string vacua, and explore the implications of a recently defined quasi-local mass which satisfies all known consistency conditions. The projects address exciting questions that have important implications for theoretical physics, and for differential and algebraic geometry. Central to the proposal is the training of postdoctoral fellows and graduate students to conduct cutting edge cross-disciplinary research and to be effective in interacting with both the physics and mathematics communities.

弦理论和引力背景下的基础物理问题通常可以纯粹地重新表述为几何问题、弦理论的真空空间，特别是超对称（BPS）物体的谱。在真空模空间的某些“壁”上，BPS 物体可以衰变成质量较小的 BPS 物体。这种穿墙现象有着极其丰富而神秘的数学结构。建议从不同角度研究穿墙，包括具有大量超对称性的真空，应用镜像对称和弦对偶性工具。 了解 BPS 天体的光谱对于计算黑洞熵和拓扑弦理论非常重要。 PI 提议揭示新的几何不变量，这些几何不变量对于物理表征这些弦真空是必要的，并探索最近定义的满足所有已知一致性条件的准局部质量的含义。 这些项目解决了对理论物理学、微分几何和代数几何具有重要影响的令人兴奋的问题。 该提案的核心是培训博士后研究员和研究生进行前沿的跨学科研究，并有效地与物理和数学界进行互动。