RUI: Amplitudes in Gauge theory and Gravity

该奖项资助鲍登学院 Stephen Naculich 教授的研究活动。Naculich 教授的研究是全球理论基本粒子物理学家持续努力的一部分，旨在开发数学模型来解释物质最小成分（所谓的“基本粒子”）的性质和行为。 更具体地说，这项研究旨在开发更有效的数学工具来计算一类称为“规范理论”的现有理论的预测，并将这些方法扩展到更一般的理论。 这项研究的第二个目标是一方面探索规范理论与描述引力子（负责重力的粒子）行为的理论之间的联系。 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。 因此，这项研究将通过促进科学在其最基本方向之一的进步来促进国家利益：发现和理解新的物理定律。 该项目预计还将产生更广泛的影响，因为它整体上涉及本科生的参与。 因此，它将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、群论和量子场论等不同主题，为他们的教育做出贡献。 这种参与将鼓励和培养高素质学生在关键科学领域的研究生学习和职业生涯。 用更专业的术语来说，该项目将重点研究规范理论和引力中微扰散射振幅的结构以及它们之间的关系。 特别是，该研究将继续探索最近发现的规范理论振幅的“颜色因子对称性”，特别是在环路水平，其扩展到更一般的理论，以及它与颜色运动二元性的关系。 该项目将进一步研究规范理论和涉及大质量粒子的重力振幅的 Cachazo-He-Yuan 表示，以及环级振幅，特别关注红外发散。 这项研究将扩展对有效场论中算子分类的研究，有助于辅助定理和辅助软定理。 最后，该项目将继续探索引力散射振幅的雷格极限，重点关注与红外发散和软定理的相互作用，以及与规范理论中类似问题的关系。

This award funds the research activities of Professor Stephen Naculich at Bowdoin College.The research of Professor Naculich 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 (the so-called "elementary particles"). More specifically, this research aims at developing more efficient mathematical tools for calculating the predictions of a certain class of existing theories known as "gauge theories", and extending these methods to more general theories. A second goal of this research is to explore links between gauge theories on the one hand, and theories 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. As a result, this research will advance the national interest by promoting the progress of science in one of its most fundamental directions: the discovery and understanding of new physical law. This project is also expected to have significant broader impacts, since it integrally involves participation by undergraduate students. It therefore will contribute to their education by providing hands-on training in research methods in theoretical physics, as well as exposure to diverse topics such as quantum mechanics, group theory, and quantum field theory. Such involvement will encourage and prepare highly-talented students for graduate study and careers in critical scientific fields. In more technical terms, this project will focus on the structure of perturbative scattering amplitudes in gauge theories and gravity and the relations between them. In particular, the research will involve continued exploration of the recently discovered "color-factor symmetry" of gauge-theory amplitudes, particularly at loop level, its extension to more general theories, and its relationship to color-kinematic duality. This project will further investigate Cachazo-He-Yuan representations for gauge-theory and gravity amplitudes involving massive particles, and also loop-level amplitudes, with particular focus on infrared divergences. This research will extend the study of the classification of operators in effective field theories contributing to subleading and subsubleading soft theorems. Finally, this project will continue to explore the Regge limit of gravitational scattering amplitudes, focusing on the interplay with infrared divergences and soft theorems, and the relationship with analogous issues in gauge theory.