RUI: Amplitudes in Gauge Theory and Gravity

该奖项资助了鲍登学院Stephen Naculich教授的研究活动。理论基本粒子物理学旨在开发能够解释物质最小成分（所谓的“基本粒子”）的性质和行为的数学模型。 作为研究的一部分，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行为的现有模型的预测，这些粒子对于理解强相互作用非常重要，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。 预计该项目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，为他们的教育做出贡献。 这种参与将鼓励和准备高人才的研究生学习和职业生涯中的关键科学领域。在更技术性的术语，这个项目将集中在规范理论和引力微扰散射振幅的结构，以及它们之间的关系。 特别是，该项目将探索Regge（或非常高的能量）极限的散射振幅在非平面超对称杨米尔斯理论的所有订单的循环扩展，结合群论方法，明确的循环水平的结果，红外发散的已知结构，和程函方法。 它还将使用类似的工具研究引力和超引力中散射振幅的Regge极限，以及它与广义相对论和引力波产生中的两体问题的联系。 最后，这项研究将涉及最近发现的“颜色因子对称性”的树和回路级规范理论振幅的继续探索，其关系的颜色运动学的对偶性在一般规范theors.This奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

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.