CAREER: Quantum Field Theory in Diverse Dimensions, Supersymmetry, and Quantum Gravity

Harvard University, Cambridge MA

Investigators

Abstract

This research program is about quantum field theory, string theory and quantum gravity, greatly strengthening the thoretical understanding of our physical universe. One focus is on finding new general properties of strongly interacting quantum field theories, new exact results in supersymmetric (relating bosonic and fermionic elementary particles)quantum field theories, and new insights into the maximally superconformal (2,0) theory in six dimensions. (Conformal invariance is a generalization of scale invariance that only requires that the angles between corresponding curves do not change.) Another is on discovering new concrete examples and implications for non-perturbative particle interactions of the gauge/gravity correspondence, and researching the emergence of bulk locality in Anti-de Sitter/Conformal Field Theory (AdS/CFT) space. Lastly, it will attempt to formulate the exact theory of quantum gravity in other backgrounds, such as an expanding de Sitter universe. Major progress has been made in discovering quantities that can be calculated exactly in supersymmetric theories, and much remains to be explored. The keys are finding new kinds of backgrounds in which supersymmetry is preserved, and then applying the technique of localization to obtain an exact reduction of the path integral to a finite dimensional integral. Such methods have given a window into the structure of the (2,0) theory, which puts its further elucidation within possible reach. The research involves the quantum entanglement entropies that give a monotonic function of scale in quantum field theories and probe the geometric structure of the emergent bulk in AdS/CFT. Nonlocal quantities such as the sphere partition function and entanglement entropy control renormalization group flows in odd dimensions implying that topological and propagating degrees of freedom are combined in a novel way. One direction of this project is to find examples of such behavior as well as new general constraints on renormalization group flows. Intellectual Merit : One of the most important open questions in theoretical quantum field theory is the determination of their dynamics at strong coupling. The new exact results for supersymmetric theories that are expected will lead to new insight into such systems. It also gives new checks of AdS/CFT and other dualities. Further explorations of quantities like the number of degrees of freedom that constrain renormalization group flows in three dimensions will lead to interesting new predictions for long distance behavior that may arise in condensed matter systems. Entanglement entropies have been playing an intriguing role in this context, and further exploring their general properties will lead to new advances. The discovery of a calculable description of the maximally superconformal theory in six dimensions will lead to new advances in understanding of supersymmetric theories in lower dimensions. Finding the general characterization, observables in arbitrary quantum states, of conformal field theory (CFT) operators that correspond to bulk will have significant implications for quantum gravity. It will be a step in understanding quantum gravity in general backgrounds, and would shed light on the black hole information paradox. New examples of AdS/CFT, and further understanding how the dualities involving the simplest conformal field theories fit into string theory will provide a window into the basic structure of the gauge/gravity correspondence. Advances in the problem of understanding the theory of quantum gravity in de Sitter space will shed light on this deep question relevant to our own expanding universe. Broader Impacts : This research allows participation in the Boston area Theorynet program, delivering biannual talks to high school classrooms. This is a good way to impart the enthusiasm for discovering new fundamental laws of physics and the importance of scientific curiosity in general. The theoretical research in strongly interacting quantum field theories also has interdisciplinary connections to condensed matter physics, as well as quantum gravity and high energy theory. The subject of entanglement entropy makes a great special topics graduate course. It is relevant to information theory, condensed matter physics, quantum field theory and quantum gravity. Lastly, through this research, finding new exact results in supersymmetric quantum field theories makes excellent manageable yet novel research projects for graduate students and postdocs.