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

University Of Kentucky Research Foundation, Lexington KY

Investigators

Abstract

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.