Topics in String Theory

该奖项资助了加州大学洛杉矶分校的埃里克·德霍克、迈克尔·古特佩尔和佩尔·克劳斯教授的研究活动。支配基本粒子定律的量子场论，以及用时空曲率表示引力的爱因斯坦广义相对论，都能准确地描述从对撞机物理到宇宙学的几乎所有观察到的物理现象。弦理论是一个令人信服的框架，可以将这些原理整合到一个统一的框架中，然而，尽管经过几十年的努力，弦理论的基本结构仍然知之甚少。一个关键因素被认为是全息原理，它将量子场论与弦理论在一个更高的维度上联系起来。D‘Hoker、Gutperle和Kraus教授的研究旨在加深我们对弦理论的理解，并通过全息术发展它与量子场论的联系。他们的研究将应用于黑洞和凝聚态物质等不同的物理系统，以及纯数学，从而通过进一步促进美国基础科学的进步来服务于国家利益。这个项目也将产生重大的更广泛的影响。D‘Hoker、Gutperle和Kraus教授将以高度合作的方式开展研究，让研究生和博士后参与，从而为物理学家在研究生涯的早期阶段提供关键培训。他们还计划通过举办研讨会、座谈会和公开讲座来传播他们的研究成果，包括在高中和暑期学校。此外，他们还参与推进教育、外展和跨学科合作。更具体地说，将解决以下问题。我们将研究弦的双环散射幅度，并将其应用于确定低能有效相互作用和颜色-运动二象性。弦理论要研究的其他方面包括自举方法和时空作用量的世界表定义。我们将构建新的超重力理论的渐近ADS解，并将其应用到缺陷、界面和超共形场理论的物理中。还将获得与量子引力和ADS/CFT基本问题相关的进一步解决方案，包括虫洞和岛屿。最后，将在有限表面上发展具有固定度量边界条件的纯重力；要计算的量子可观测包括边界应力张量的能谱和关联函数，这两者都将与由无关算符变形的共形场论的类似结果进行比较。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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 Professors Eric D'Hoker, Michael Gutperle, and Per Kraus at the University of California, Los Angeles.Quantum field theory, which governs the laws of elementary particles, and Einstein's theory of General Relativity, which formulates gravity in terms of spacetime curvature, are known to accurately describe almost all observed physical phenomena from collider physics to cosmology. String theory is a compelling framework for incorporating these principles in a unified framework, yet despite decades of effort the fundamental structure of string theory remains poorly understood. A key ingredient is believed to be the holographic principle, relating quantum field theories to string theory in one higher dimension. The research of Professors D'Hoker, Gutperle, and Kraus is aimed at deepening our understanding of string theory, as well as developing its connection to quantum field theory through holography. Their research will have applications to such diverse physical systems as black holes and condensed matter as well as to pure mathematics, thereby serving the national interest by further the progress of basic science in the United States. This project will also have significant broader impact. Professors D'Hoker, Gutperle, and Kraus will be conducting research in a highly collaborative manner involving graduate students and postdocs, thereby providing critical training for physicists in the early stages of their research careers. They also plan to disseminate the results of their research by presenting seminars, colloquia, and public lectures, including at high schools and summer schools. Additionally, they are involved in advancing education, outreach, and interdisciplinary collaboration.More specifically, the following problems will be addressed. Two-loop scattering amplitudes of strings will be studied and applied to the determination of low-energy effective interactions and to color-kinematics duality. Other aspects of string theory to be studied include a bootstrap approach and the worldsheet definition of the spacetime action. New asymptotically AdS solutions to supergravity theories will be constructed, with applications to the physics of defects, interfaces, and superconformal field theories. Further solutions relevant to foundational issues in quantum gravity and AdS/CFT, including wormholes and islands, will also be obtained. Finally, pure gravity with fixed metric boundary conditions on a finite surface will be developed; quantum observables to be computed include the energy spectrum and correlation functions of the boundary stress tensor, both of which will be compared against analogous results from conformal field theories deformed by an irrelevant operator.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.