Geometry and Vacuum Structure in String Theory

PI将使用一系列物理和数学技术研究弦理论中当前感兴趣的问题，如模稳定性、亚稳态真空、膜量子化和黑洞热力学。智力优势拟议的研究包括三个项目，涉及弦理论和数学物理的不同领域。第一个项目的目的是寻找弦理论中稳定和亚稳定真空的新结构以及新的Kahler模稳定机制。这些问题对于全面理解弦理论是至关重要的。第二个项目的目标是利用大N对偶、非对易代数几何和可积系，找到全纯膜，或者等价地，Calabi-Yau三重上的派生对象的代数量子化方案。第三个项目是基于高维规范理论中的Atiyah-Bott局域化，寻找带磁荷的弦理论黑洞的微观描述。更广泛的影响这项工作中涉及的问题在物理和数学中有更广泛的影响。理解弦理论的前景，特别是真空选择机制，将立即对弦宇宙学、弦现象学和量子引力产生影响。极值跃迁和大N对偶性已经对某些数学领域产生了相当大的影响，例如Gromov-Witten理论和纽结理论。PI旨在探索大N对偶性在其他领域的影响，如派生范畴、可积系统和强调跨学科研究方法的全纯量子化。同样，寻找黑洞自由度的微观描述也是理论物理中的一个基本问题。PI提出了一种基于局部化、代数几何和物理的相互作用的新方法来解决这个问题。这项工作的成果将在跨学科会议、研讨会和讲习班上介绍。本提案中讨论的项目以具体计算、小型独立分项目、非正式口头报告和学习小组的形式为本科生和研究生提供了许多培训机会。这些活动的目的是招收具有很高研究潜力的学生，并发展即使在学术界以外也非常有价值的科学技能。

The PI will investigate questions of current interest in string theory, such as moduli stabilization, metastable vacua, brane quantization and black hole thermodynamics using an array of physical and mathematical techniques. Intellectual Merits The proposed research consists of three projects addressing different areas of string theory and mathematical physics. The first project is aimed at finding new constructions of stable and metastable vacua in string theory as well as new Kahler moduli stabilization mechanisms. These problems are essential for a complete understanding of the string theory landscape. The goal of the second project is finding an algebraic quantization scheme for holomorphic branes, or, equivalently, derived objects on Calabi-Yau threefolds, using large N duality, noncommutative algebraic geometry and integrable systems. The third project aims at finding a microscopic description of string theory black holes with magnetic charge based on Atiyah-Bott localization in higher dimensional gauge theory. Broader Impact The questions addressed in this work have a broader impact in physics and mathematics. Understanding the string theory landscape and especially vacuum selection mechanisms will have immediate impact in stringy cosmology, stringy phenomenology and quantum gravity. Extremal transitions and large N duality have already had a considerable impact on certain areas of mathematics such as Gromov-Witten theory and knot theory. The Pi intends to explore the impact of large N duality in other areas such as derived categories, integrable systems and holomorphic quantization emphasizing interdisciplinary research methods. Similarly, finding a microscopic description of black hole degrees of freedom is a fundamental question in theoretical physics. The PI proposes a new approach to this problem based on an interplay of localization, algebraic geometry and physics. The results of this work will be presented at interdisciplinary conferences, seminars and workshops. The projects discussed in this proposal offer many training opportunities for undergraduate and graduate students in the form of concrete computations, small self-contained subprojects, informal oral presentations and study groups. These activities will be aimed at recruiting students showing high research potential and developing scienti c skills which can be very valuable even outside the academic community.