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

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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.