NSF-BSF: New Approaches to Conformal Field Theory - Codes, Ensembles, and Complexity

这个NSF-BSF奖资助了肯塔基大学Anatoly Dymarsky教授的研究活动。量子场论是我们对基本粒子及其相互作用的现代理解的理论框架。几十年来，它一直受到科学界的持续关注，科学界试图阐明其最基本的原理和含义。这种探索一直持续到今天。然而，事实证明，量子场论展示了极其丰富的数学结构，不断产生新的见解，并与其他科学分支建立联系。最近表现出快速发展的领域之一是量子场论和量子信息论之间的联系，量子信息论是研究量子系统如何包含和处理信息的科学分支。作为他研究的一部分，Dymarsky教授将研究量子场——量子场论的基石——如何用量子和经典信息来描述和表征。该项目主要关注该领域的几个问题，将与以色列科学家共同进行，美国国家科学基金会支持美国方面的合作。该项目还通过扩展关于物理基本定律的知识前沿，为实现国家利益的目标做出贡献。最后，该项目还将有助于物理教育，并增加代表性不足群体成员在STEM研究中的参与。本研究更广泛的影响目标包括通过美国国家科学基金会“本科生研究经验”计划的框架对物理学本科生进行专业培训。从技术上讲，该研究项目涉及从信息论和理论计算机科学到量子场论的几个关键概念的应用。首先是“代码”的概念，这是压缩和保存常规电信系统中经常使用的信息的数学框架。具体来说，作为该项目的一部分，Dymarsky教授将研究如何使用代码来描述和研究二维共形场理论。其次是复杂性的概念，它描述了实现算法或破译一条信息所涉及的实际困难。这个概念在场论中有很多应用，作为该项目的一部分，Dymarsky教授将研究评估复杂性的不同定义和处方是如何相互关联的。该项目的其他具体目标包括将信息论应用于最近引入的基于全息通信的集成解释。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 NSF-BSF award funds the research activities of Professor Anatoly Dymarsky at the University of Kentucky.Quantum field theory is the theoretical framework underlying our modern understanding of the elementary particles and their interactions. For many decades it has enjoyed the constant attention of the scientific community which has attempted to lay out its most basic principles and implications. This quest continues to this day. However, as it turns out, quantum field theory exhibits extraordinarily rich mathematical structures, constantly giving rise to new insights and connections with other branches of science. One of the areas exhibiting rapid development recently is the connection between quantum field theory and quantum information theory --- a branch of science studying ways in which quantum systems can contain and process information. As part of his research, Professor Dymarsky will investigate how quantum fields --- the building blocks of quantum field theory --- can be described and characterized in terms of quantum and classical information. This project focuses on several questions within this area and will be pursued jointly with scientists from Israel, with NSF supporting the American side of this collaboration. This project also contributes to goals of national interest by extending the frontiers of knowledge regarding the fundamental laws of physics. Finally, this project will also contribute to physics education and increase the participation of members of underrepresented groups in STEM research. Broader-impact goals of this research include the professional training of undergraduate physics students through the framework of the NSF "Research Experiences for Undergraduates" program. More technically, this research project addresses applications of several key concepts stretching from information theory and theoretical computer science to quantum field theory. First is the notion of "codes", a mathematical framework for compressing and preserving information routinely utilized in conventional telecommunications systems. Specifically, as part of this project, Professor Dymarsky will investigate how codes can be used to describe and study two-dimensional conformal field theory. Second is the notion of complexity, which characterizes the practical difficulty involved in implementing an algorithm or deciphering a piece of information. This notion finds many applications in field theory, and as part of this project Professor Dymarsky will study how different definitions and prescriptions for evaluating complexity are related to each other. Other specific goals of this project include applying information theory to the recently-introduced ensemble-based interpretation of the holographic correspondence.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.