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

半个世纪来，黑洞一直吸引着物理学家和数学家。 尽管进行了深入的研究，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试图更好地理解黑洞的奥秘。超对称黑洞起源于弦理论的卡-丘紧化。 一个精确的拓扑弦振幅（或Gromov-Witten不变量）的卡拉比-威滕计算之间的关系进行，并发现是在完全符合的猜想。 它被提议为这个新理论提供基础，并极大地扩展几何学与弦理论之间的这些新联系，在这个过程中丰富了这两个领域。 在过去的几年里，人们发现了黑洞的微观成分与流形内体积最小的循环之间的深刻联系。 这将黑洞的谜题与许多数学上有趣的问题联系起来，包括特殊的拉格朗日子流形，全纯曲线等，这些被广泛称为拓扑弦。 该项目试图更深入地了解拓扑弦和黑洞之间的联系。这很可能对物理学和数学都有重要的影响。 主要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为开展拟议的研究做好了充分的准备。

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.