RUI: Supersymmetric Gauge Theory and String Theory

该奖项资助了位于缅因州不伦瑞克的鲍登学院（Bowdoin College）的纳库利奇教授的研究活动。这项研究是世界范围内理论基本粒子物理学家开发数学模型来解释物质最小组成部分（基本粒子）的性质和行为的持续努力的一部分。更具体地说，这项研究旨在开发更有效的数学工具来计算现有的夸克和胶子模型的预测，这些模型被称为“规范理论”。这项研究的第二个目标是探索规范理论与描述引力子（产生引力的粒子）行为的理论（如超引力理论和弦理论）之间的联系。通过这项研究获得的见解将通过期刊出版物、研讨会和会议记录进行传播。这项研究也需要本科生的参与，因此，通过提供理论物理研究方法的实践培训，以及接触量子力学、群论和量子场论，将有助于他们的教育。这种参与将鼓励和培养高素质的学生在研究生学习和科学领域的职业生涯。用更专业的术语来说，这个项目关注超对称规范理论和超引力理论的微扰和非微扰方面，正如它们与弦理论的联系所阐明的那样。特别是，本研究将探索树级和环级规范理论散射振幅之间的约束，这些约束对规范理论是通用的，与理论的物质内容无关。这既包括仅依赖于规范群的约束，也包括Bern-Carrasco-Johansson型关系。本研究将进一步研究1/N膨胀中次级的环级SU(N)规范理论幅值的结构、红外散度以及这些幅值之间潜在的迭代结构。最后，该项目将研究超重力振幅的结构，它们的红外发散，以及超重力和超对称杨-米尔斯振幅在环路水平上的潜在关系。

This award funds the research activities of Professor Naculich at Bowdoin College, an undergraduate institution located in Brunswick, Maine. This research is part of an on-going effort by the worldwide community of theoretical elementary particle physicists to develop mathematical models to explain the nature and behavior of the smallest constituents of matter (elementary particles). More specifically, this research aims at developing more efficient mathematical tools for calculating the predictions of existing models of quarks and gluons called "gauge theories". A second goal of this research is to explore links between gauge theories on the one hand, and theories (such as supergravity and string theory) that describe the behavior of gravitons, the particles responsible for the force of gravity, on the other. The insights gained through this research will be disseminated through journal publications, seminars, and conference proceedings. This research also integrally involves participation by undergraduates, and will therefore contribute to their education by providing hands-on training in research methods in theoretical physics, as well as exposure to quantum mechanics, group theory, and quantum field theory. Such involvement will encourage and prepare highly-talented students for graduate study and careers in scientific fields.In more technical terms, this project focuses on both perturbative and non-perturbative aspects of supersymmetric gauge theory and supergravity theory, as illuminated by their connection to string theory. In particular, this research will explore constraints among tree-level and loop-level gauge theory scattering amplitudes that are generic to gauge theory, independent of the matter content of the theory. These include both constraints that depend only on the gauge group, as well as Bern-Carrasco-Johansson type relations. The research will further investigate the structure of loop-level SU(N) gauge theory amplitudes that are subleading in the 1/N expansion, their infrared divergences, and potential iterative structures among these amplitudes. Finally, the project will study the structure of the amplitudes of supergravity, their infrared divergences, and potential relations between supergravity and supersymmetric Yang-Mills amplitudes at the loop level.