Scale Invariance in Quantum Field Theory

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This award funds the research activities of Professor Anatoly Dymarsky at the University of Kentucky.The proposed research program concerns quantum field theory, the universal theoretical framework for describing the dynamics of the elementary particles. Among the multitude of different field-theoretic models there are those which are simpler, more fundamental, and which include no dimensionful parameters. The goal of this project is to advance our current understanding of such quantum field theories without internal scales by developing new theoretical approaches that do not rely on the assumption that the interactions between the elementary particles are weak. The results obtained will be used to further clarify the mechanism by which continuous systems reach equilibrium. Thus, this project serves the national interest by extending our current knowledge of fundamental science in areas pertaining to basic properties of quantum field theory, which has application across many fields of science. This project is also envisioned to have significant broader impacts. One of the goals of this project is to enhance the quality of graduate and post-graduate physics education through the involvement of graduate students and young researchers. Furthermore, this research will contribute toward our understanding of nature at the fundamental level, which is of interest to the general public. The PI is also actively engaged in promoting elementary-particle physics by giving public lectures and working together with a group of film producers developing a science-fiction TV series popularizing modern physics.On a more technical level, the goal of this project is to study quantum field theories without internal scales. The focus on scale-invariant models is justified by an extended symmetry providing additional theoretical control as well as the fundamental role these models play in defining other theories through appropriately chosen deformations. The specific aims of the project can be divided into three broad categories: to investigate the connection between scale and conformal invariance in quantum field theory and identify characteristic properties of scale-invariant non-conformal field theories; to develop a theory of thermalization in the context of quantum field-theoretic systems, and in particular to extend the Eigenstate Thermalization Hypothesis to continuous systems; and to improve our understanding of the universal properties of conformal field theories. These objectives will be achieved by a combination of non-perturbative methods such as the holographic correspondence, conformal bootstrap, and methods of quantum information theory.