Studying Special Holonomy Manifolds Using Conformal Field Theory Tools

该奖项资助奥尔巴尼大学的丹尼尔罗宾斯教授的研究活动。共形场论（英语：Conformal field theories）（CFT）在物理学中被用来描述相变（例如冰融化成水），或者理解在非常低或非常高的能量下量子理论中发生的事情。 CFT在弦理论中也扮演着核心角色，弦理论是统一所有自然基本力的引力量子理论的主要候选者。 在不同几何空间中运动的弦由不同的CFT描述，这反过来又导致不同的物理现象和性质。 本研究计划将探讨CFT的，几何形状和由此产生的物理定律之间的联系。 这项工作通过促进物理学和数学之间跨学科边界的基础科学的进步，从而加强美国的基础科学，从而促进国家利益。 研究生和本科生也将参与这个项目，接受罗宾斯教授的研究培训，并有机会向其他研究人员展示他们的工作。在更技术的层面上，这个项目将把最近开发的CFT技术应用于一类由特殊完整流形构建的超共形场论（SCFT）。共形引导程序和模块化引导程序的哲学和工具，这两个程序都利用CFT一致性条件，以获得对CFT定义数据的约束，将用于找到对一类流形的几何数据的约束，这些流形在弦理论中起着重要作用，并探索它们的模空间和相应的弦理论结构的物理性质。该项目还将把最近的想法和工具从CFT缺陷的研究应用到同类的SCFT，研究由畴壁，边界SCFT，相关弦理论中的D膜连接的理论之间的联系，该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的知识产权评估的支持。优点和更广泛的影响审查标准。

This award funds the research activities of Professor Daniel Robbins at the University at Albany. Conformal field theories (CFT's) are used in physics to describe phase transitions (such as ice melting into water), or to understand what happens in a quantum theory at very low or very high energies. CFT's also play a central role in string theory, which is the leading candidate for a quantum theory of gravity that unifies all of the fundamental forces of nature. Strings moving in different geometrical spaces are described by different CFT's that in turn lead to different physical phenomena and properties. This research program will explore the connections between CFT's, geometry, and the resulting physical laws. This work advances the national interest by fostering the progress of fundamental science at the interdisciplinary boundary between physics and mathematics, and thereby strengthening fundamental science within the United States. Students, both graduate and undergraduate, will also be involved in this project, receiving research training from Professor Robbins and receiving opportunities to present their work to other researchers.On a more technical level, this project will apply recently developed CFT techniques to a class of superconformal field theories (SCFT's) constructed from special holonomy manifolds. The philosophy and tools of the conformal bootstrap program and the modular bootstrap program, both of which exploit CFT consistency conditions in order to derive constraints on the defining data of a CFT, will be used to find constraints on the geometrical data of a class of manifolds that play an important role in string theory, and to explore aspects of their moduli spaces and the physical properties of the corresponding string theory constructions. The project will also apply recent ideas and tools from the study of CFT defects to the same class of SCFT's, investigating connections between theories connected by domain walls, boundary SCFT's, D-branes in the associated string theories, and the study of mathematical invariants of special holonomy manifolds.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.