Defects and Extended Objects in Quantum Field Theory and Quantum Gravity

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This award funds the research activities of Professor Yifan Wang at New York University.Matter rarely appears in nature as a pure substance. More commonly it exists as a complex mixture of multiple components. In cases when the matter is almost homogenous, the remaining irregularities or discontinuities are known as defects. Examples of physically interesting defects range from those encountered in daily life such as fat droplets suspended in milk and impurity atoms in metals, to extreme scenarios such as heavy particles in an exotic state of matter known as the quark-gluon plasma where immense heat and pressure crush the nuclei to make a soup of elementary particles. It has been found that defects have profound consequences for the physical behavior of the materials, give rise to novel phase transitions and critical phenomena, and provide sensitive probes for detecting phases of matter. An important challenge in theoretical physics is to develop tools to analyze defects and their properties. Quantum field theory, which is arguably the most successful physical theory for systems with a large number of constituent elements, provides the natural framework to describe defects. However much of the success of quantum field theory dwells on the fundamental principles of symmetry and locality, and to incorporate defects requires a refinement of these principles. This in turn uncovers an abundance of intricate mathematical structures to be understood. Professor Wang aims to advance the understanding of defects in quantum field theory by pursuing the following questions: How do we predict the effects from the defects? Are there universal patterns in the properties of defects? Are there principles behind how defects behave? Addressing these questions would promote the progress of science and advance the national interest by potentially discovering and understanding new physical laws. Professor Wang's work will also produce broader impacts in the form of the development of new courses, training undergraduate and graduate physics students, as well as mentoring postdoctoral researchers through collaborations on these projects.More technically, Professor Wang aims to pursue a thorough investigation of defects in quantum field theory from multiple complementary angles. This includes deriving universal constraints to delineate the landscape of admissible defects, developing analytic tools to access defect observables and clarify their features, and exploring generalized symmetries and anomalies from defects. By the celebrated holographic duality, defects in ordinary quantum many-body systems are also closely related to extended objects in quantum gravity, known as branes (such as D-branes in string theory). These branes are essential for the consistency of quantum gravity at the non-perturbative level, but the spectrum and dynamics of such branes remain under-explored. In parallel to his field-theoretic exploration of defects, Professor Wang also plans to deduce consequences for the non-perturbative branes in quantum gravity. To achieve the aforementioned goals, a combination of techniques will be employed and further developed along the way, including conformal bootstrap, topological field theory, supersymmetry, integrability, and large-N limits. One immediate impact of the proposed work will be an integrated perspective of the extended operator algebra in quantum field theory that incorporates defects, and an improved understanding of renormalization-group flows in both high-energy and condensed-matter systems. Another promising outcome would be a systematic analysis of (non-supersymmetric) D-branes in string theory and more general extended objects in quantum gravity.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.