NSF-BSF: New Approaches To Conformal Field Theory - Codes, Ensembles, And Complexity

The proposed research is about quantum field theory – a theoretical framework to describe fundamental forces and interactions. The goal of the proposed activities is to develop novel approaches to study out-of-equilibrium dynamics of quantum field theory, and apply them towards elementary particle physics and quantum gravity. The specific goals of the proposal fall into several broad categories. First is to advance current understanding of two-dimensional conformal field theories. Second is to develop new quantitative methods to characterize complexity and chaotic behavior of quantum systems. Third is to connect quantum field theory with topics of discrete mathematics and quantum information theory. These objectives will be achieved by a variety of methods, including holographic correspondence, quantum integrability, and numerical simulations. This is an NSF-BSF proposal, submitted jointly by the US PI to NSF and by the Israeli co-PIs to the US-Israel Binational Science Foundation (BSF). The proposed activities assume an active collaboration between the US PI with the Israeli counterparts, Prof. Smolkin of the Hebrew University of Jerusalem and Prof. Carni of Technion, who will contribute there expertise in such areas as quantum complexity, dynamics in Krylov space, and quantum field theory in general. Intellectual Merit The proposed activities will advance current knowledge of fundamental physics in the area of non-equilibrium dynamics of quantum field theory. New approaches and results in the area of non-equilibrium dynamics will have important applications toward strongly-coupled interactions of elementary particles. New quantitative ways to characterize quantum chaos are important for a number of research topics, ranging from the systems of correlated electrons, to quantum algorithms, to black hole physics. Progress in understanding mathematical structure of conformal field theory is of interdisciplinary value. It establishes new connections between quantum field theory, String Theory, and discrete mathematics. Broader Impacts The broader impact goals of this proposal are to facilitate participation of undergraduate students in STEM research, enhance the quality of graduate and post-graduate physics education, and increase awareness of modern physics by the general public. Professional development of graduate students and postdoctoral scholars is an internal part of this proposal, which includes a number of concrete projects designed specifically for young researchers. The PI will provide supervision and will work closely with graduate students and postdoctoral scholars at all stages of the project. The proposed activities will enhance and broaden the frontier physics research in the Central Kentucky area.