RUI: Amplitudes in Gauge Theory and Gravity

该奖项资助鲍登学院斯蒂芬·纳库利奇教授的研究活动。理论基本粒子物理学寻求发展数学模型来解释物质的最小组成部分（即所谓的“基本粒子”）的性质和行为。作为他研究的一部分，Naculich教授的目标是开发更有效的数学工具，用于计算描述夸克和胶子（对理解强相互作用很重要的粒子）行为的现有模型的预测，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探索这些理论与描述引力子行为的理论之间的联系，引力子是负责引力的粒子。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的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。该项目还有望产生更广泛的影响，因为它全面涉及本科生的参与。因此，它将通过提供理论物理研究方法的实践培训，为他们的教育做出贡献。这种参与将鼓励和培养高素质的学生在关键科学领域的研究生学习和职业生涯。在更技术性的术语中，本项目将侧重于规范理论和重力中微扰散射振幅的结构，以及它们之间的关系。特别地，本项目将结合群论方法、显式环能级结果、已知的红外发散结构和eikonal方法，探索非平面超对称杨-米尔斯理论在环展开中所有阶散射振幅的Regge（或极高能量）极限。它还将使用类似的工具，研究重力和超重力散射振幅的Regge极限，以及它与广义相对论中的二体问题和引力波产生的联系。最后，本研究将继续探索最近发现的树级和环级规范理论振幅的“颜色因子对称性”，以及它与一般规范理论中颜色-运动学对偶的关系。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award funds the research activities of Professor Stephen Naculich at Bowdoin College.Theoretical elementary particle physics seeks to develop mathematical models that can explain the nature and behavior of the smallest constituents of matter (the so-called "elementary particles"). As part of his research, Professor Naculich aims to develop more efficient mathematical tools for calculating the predictions of existing models that describe the behaviors of quarks and gluons, particles that are important for understanding the strong interaction, and extending these methods to more general theories. A second goal of this research is to explore links between these sorts of theories and theories that describe the behavior of gravitons, the particles responsible for the force of gravity. 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 laws. This project is also expected to have significant broader impacts, since it integrally involves participation by undergraduate students. It will therefore contribute to their education by providing hands-on training in research methods in theoretical physics. 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 project will explore the Regge (or very high energy) limit of scattering amplitudes in nonplanar supersymmetric Yang-Mills theory to all orders in the loop expansion, combining group theory methods, explicit loop-level results, the known structure of infrared divergences, and eikonal methods. It will also investigate, using similar tools, the Regge limit of scattering amplitudes in gravity and supergravity, and its connection with the two-body problem in general relativity and gravitational wave generation. Finally, this research will involve the continued exploration of the recently discovered "color-factor symmetry" of tree- and loop-level gauge-theory amplitudes, and its relationship to color-kinematic duality in general gauge theories.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.