Supersymmetric Field Theories from F-Theory

该奖项资助了加州大学圣巴巴拉分校的大卫·莫里森教授的研究活动。自然界中一些最有趣的现象是用物理理论描述的，在这些理论中，相互作用同时发生在许多不同的距离尺度上。这些所谓的“共形场理论”对于理解各种各样的现象至关重要，从半导体工业中使用的材料的行为，到引力微观(量子力学)性质背后的物理基础。由于相互作用的规模是如此的多样化，这些理论不能用传统的理论工具来描述，本项目的目的是开发改进的理论工具，以便更好地理解这些系统。这项研究通过促进我们对可能有许多广泛应用的系统的基本科学知识来促进国家利益。预计该项目还将产生更广泛的重大影响。莫里森教授将让研究生和博士后参与他的研究，从而为开始这一领域研究的初级科学家提供关键培训。他还打算通过努力向广大公众广泛提供科学文献来促进公众对科学的理解。在技术上，莫里森教授将使用F理论和椭圆纤颤的代数几何来研究四维和六维的超对称共形场论。F理论是超弦理论的变种，它严重依赖于代数几何的构造(在数学中)来产生所需的物理效果。莫里森教授将利用代数几何来开发新的F理论工具，并以这种方式提高我们对六维共形场理论的理解。他还将利用一种从六维理论产生四维理论的通用方法，使该方法适应F理论的背景。

This award funds the research activities of Professor David Morrison at the University of California, Santa Barbara.Some of the most interesting phenomena in nature are described by physical theories in which interactions happen at many different distance scales at once. These so-called "conformal field theories" are crucial for understanding diverse phenomena ranging from the behavior of materials such as those used in the semiconductor industry to the physics underlying the microscopic (quantum-mechanical) nature of gravity. Because the interaction scales are so diverse, these theories cannot be described using conventional theoretical tools, and this project is aimed at developing improved theoretical tools in order to achieve a better understanding of these systems. This research advances the national interest by furthering our basic scientific knowledge of systems that are likely to have numerous broad-ranging applications. This project is also envisioned to have significant broader impacts. Professor Morrison will involve graduate students and postdocs in his research, and thereby provide critical training for junior scientists beginning research in this field. He also intends to promote the public understanding of science through efforts to make the scientific literature broadly available to the public at large. More technically, Professor Morrison will investigate supersymmetric conformal field theories in dimensions four and six by using F theory and the algebraic geometry of elliptic fibrations. F-theory is a variant of a superstring theory which relies heavily on constructions from algebraic geometry (in mathematics) to produce desired physical effects. Professor Morrison will use algebraic geometry to develop new F-theory tools and improve our understanding of six-dimensional conformal field theories in this way. He will also utilize a general method for producing four-dimensional theories from six-dimensional ones, adapting that method to the F theory context.