Collaborative Research: Geometry of Black Hole Entropy, Special Lagrangians, and Topological String Theory

合作研究：黑洞熵几何、特殊拉格朗日量和拓扑弦理论

• 批准号: 0628341
• 负责人: Cumrun Vafa
• 金额: $ 13万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0628341&HistoricalAwards=false
• 关键词: Collaborative; Research; Geometry; Black; Hole

Black holes have fascinated physicists and mathematicians for half a century. Despite intensive research, they remain one of the most enigmatic objects in the universe. Many important theoretical breakthroughs in physics have resulted from attempts at a better understanding of the mysteries of black hole. Supersymmetric black holes arise from Calabi-Yau compactifications of string theory. A precise relation between topological string amplitudes (or Gromov-Witten invariants) of the Calabi-Witten computations were performed and found to be in complete agreement with the conjecture. It is proposed to provide the foundations of this new theory and greatly expand on these new connections between geometry and string theory, in the process enriching both fields. In the past few years a deep connection has been found between microscopic constituents of black holes and cycles with minimal volume inside manifolds. This connects puzzles of black holes to many mathematically interesting questions, including special Lagrangian submanifolds, holomorphic curves, etc. These are broadly known as topological strings. The project is an attempt to more deeply understand the link between topological strings and black holes. This will very likely have important ramifications both for physics and mathematics. The principal investigators have already made some of the pioneering investigations in this regard and with their active research groups are well equipped to carry out the proposed research.

半个世纪以来，黑洞一直让物理学家和数学家着迷。尽管进行了密集的研究，它们仍然是宇宙中最神秘的物体之一。物理学中许多重要的理论突破都是由于人们试图更好地理解黑洞的奥秘。超对称黑洞起源于弦理论的Calabi-Yau紧致化。给出了Calabi-Witten计算的拓扑弦振幅(或Gromov-Witten不变量)之间的精确关系，发现与猜想完全一致。建议提供这一新理论的基础，并在丰富这两个领域的过程中，极大地扩展几何和弦理论之间的这些新联系。在过去的几年里，人们发现黑洞的微观成分与流形内部体积最小的旋回之间存在着深刻的联系。这将黑洞的谜题与许多数学上有趣的问题联系在一起，包括特殊的拉格朗日子流形、全纯曲线等。这些问题被广泛地称为拓扑弦。该项目试图更深入地理解拓扑弦和黑洞之间的联系。这很可能会对物理学和数学产生重要的影响。首席调查人员已经在这方面进行了一些开创性的调查，他们的积极研究小组已经做好了开展拟议研究的准备。