Geometry and Vacuum Structure in String Theory

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.