Research in String Theory and Field Theory

该奖项资助肯塔基大学Sumit R.Das教授的研究活动。量子力学描述了原子、原子核和基本粒子微观世界中所有已知的现象。广义相对论是引力理论：它描述了从地球到天文尺度的宏观世界中的引力现象。为了获得一个连贯的、包罗万象的物理理论，有必要以一种逻辑上一致的方式将这两组定律结合起来。然而，构建这样一个一致的框架仍然是当代物理学中最重要的悬而未决的基础问题之一。这个项目旨在利用最近在量子力学和广义相对论领域获得的新见解，解决人们试图将量子力学和广义相对论结合起来时出现的几个问题。将使用的一个关键因素是“量子纠缠”-这是量子力学的一种性质，它解释了为什么在相距遥远的地方进行的测量可以以精确的方式进行关联。量子纠缠是自然界中观察到的各种物理现象的核心，也是构建量子计算机所使用的基本原理之一。因此，这项研究的结果将通过促进美国基础科学的发展来服务于国家利益。这是这个项目在智力上的主要优点。PI还将让研究生和博士后学者参与这项研究，从而为他们提供必要的宝贵培训，使他们成为独立的科学家和教育工作者。此外，这项研究的结果将用于加强研究生和本科生的课堂教育。该协会还计划在不同的论坛上就这一主题进行公开演讲，并在为社区成员提供课程和丰富课程的“Osher终身学习学院”授课。国际和平研究所还计划参与“人人有科学，肯塔基州”，这是一个设在列克星敦的外展项目，旨在提高社区的科学意识。更严格地说，达斯教授将研究全息对应的各个方面，即在较低的时空维度上将引力理论与非引力理论联系起来。这意味着空间本身是一个新出现的概念。此外，越来越清楚的是，量子纠缠在这种出现中发挥了关键作用。将开展的项目有三个主要目标。第一个是探索量子场论中最近发展起来的场空间中的纠缠概念，以及它与引力对偶中空间区域之间的纠缠概念的关系。这将在弦理论中出现的全息对应的已知例子中完成。第二个目标是在一类精确可解的模型中找到详细的全息图，这些模型是黑洞的双重描述。第三个目标是应用开发的概念和方法来了解多体系统的纠缠特性，这些特性出现在物理学的不同领域。这项研究的结果将有助于揭示全息对应的起源以及场论的内部自由度在时空中蜕变到额外维度的过程。这一奖项反映了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 Professor Sumit R. Das at the University of Kentucky.Quantum Mechanics describes all known phenomena in the microscopic world of atoms, nuclei, and elementary particles. General Relativity is the theory of gravity: it describes gravitational phenomena in the macroscopic world, all the way from terrestrial to astronomical scales. To obtain a coherent all-encompassing physical theory it is necessary to combine these two sets of laws in a logically consistent fashion. However, construction of such a consistent framework remains one of the most important unsolved foundational problems in contemporary physics. This project aims to address several issues which arise when one tries to combine Quantum Mechanics and General Relativity, using new insights which have been recently gained in both these areas. One key ingredient which will be used is "quantum entanglement" --- a property of quantum mechanics which explains why measurements made at places which are far from each other can be correlated in a precise fashion. Quantum entanglement is at the heart of a variety of physical phenomena observed in nature and is one of the basic principles used in the construction of quantum computers. Consequently, results of this research will serve the national interest by advancing fundamental science in the US. This is the main intellectual merit of this project. The PI will also involve graduate students and postdoctoral scholars in this research, thus providing them valuable training necessary to develop into independent scientists and educators. In addition, the results of this research will be used to enhance classroom education both at the graduate and undergraduate levels. The PI also plans to give public talks about this subject in various forums, and to deliver lectures at the “Osher Lifelong Learning Institute” which offers courses and enrichment programs to members of the community. The PI also plans to engage in “Science for Everyone, KY” which is an outreach program based in Lexington with an aim to increase scientific awareness in the community.More technically, Professor Das will study aspects of the Holographic Correspondence which relates gravitational theories to non-gravitational theories in a lower number of space-time dimensions. This implies that space itself is an emergent concept. Furthermore, it is becoming increasingly clear that quantum entanglement plays a key role in this emergence. The projects that will be pursued have three main goals. The first is to explore recently developed notions of entanglement in the field space in quantum field theories, and its relationship to notions of entanglement between spatial regions in their gravitational duals. This will be done in known examples of the holographic correspondence which appear in String Theory. The second goal is to find the detailed holographic map in a class of exactly solvable models which are dual descriptions of black holes. The third goal is to apply the concepts and methods developed to learn about entanglement properties of many-body systems which appear in diverse areas of physics. The results of this research will throw light on the origins of the holographic correspondence and the process in which the internal degrees of freedom of field theories metamorphose into additional dimensions in space-time.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.