Research in String Theory and Field Theory

该奖项资助Sumit R教授的研究活动。量子力学描述了原子、原子核和基本粒子的微观世界中所有已知的现象。广义相对论是引力理论：它描述了宏观世界中的引力现象，从地球到天文尺度。为了得到一个连贯的、包罗万象的物理理论，有必要以逻辑上一致的方式把这两套定律联合收割机结合起来。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未解决的基础问题之一。 本项目旨在解决当人们试图将联合收割机量子力学和广义相对论结合起来时出现的几个问题，使用最近在这两个领域获得的新见解。将使用的一个关键因素是“量子纠缠”--量子力学的一个特性，它解释了为什么在相距很远的地方进行的测量可以以精确的方式相互关联。 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的基本原理之一。 因此，这项研究的结果将通过推进美国的基础科学来服务于国家利益。 这是这个项目的主要智力价值。PI还将让研究生和博士后学者参与这项研究，从而为他们提供发展成为独立科学家和教育家所需的宝贵培训。 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。PI还计划在各种论坛上就这一主题进行公开讲座，并在“Osher终身学习研究所”举办讲座，该研究所为社区成员提供课程和充实方案。此外，PI还计划在列克星敦开展一项名为“Science for Everyone，KY”的外展计划，旨在提高社区的科学意识。更技术性的是，Das教授将研究全息对应（Holographic Correspondence）的各个方面，该对应将引力理论与较低时空维度的非引力理论联系起来。这意味着空间本身就是一个涌现的概念。此外，越来越清楚的是，量子纠缠在这一出现中起着关键作用。将实施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的场空间纠缠概念，以及它与引力场中空间区域之间纠缠概念的关系。这将在弦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黑洞对偶描述模型中找到详细的全息图。第三个目标是应用所开发的概念和方法来了解出现在物理学不同领域的多体系统的纠缠特性。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变形为额外维度的过程。该奖项反映了NSF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 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.