RUI: Solitons and Quantum Field Theory

This award funds the research activities of Professor Andy Royston at Penn State Fayette, The Eberly Campus.

The concept of a 'field' is central to physics and everyday life. Fields (such as electric fields and magnetic fields) exist throughout space and enable the transmission of forces like gravity, electricity, and magnetism. Light and radio waves, for example, are ripples in an electromagnetic field. 'Quantum field theory' is the mathematical framework theoretical physicists use to describe fundamental particles as discrete ripples in a field. In his research, Professor Royston aims to apply novel approaches centered on the use of objects called 'solitons' to address two difficult and long-standing questions in quantum field theory. A soliton is a special type of particle that can exist when fields self-interact; one can imagine a soliton as a knot of tangled-up field. By studying the mathematical description of solitons interacting with each other and with ordinary particles, Professor Royston aims to understand mechanisms for certain particle creation and decay processes beyond the reach of traditional computational methods. Research on the mathematical structure of quantum field theory thus advances the national interest by promoting the progress of science at its most foundational level. This project will also have significant broader impacts. Professor Royston will involve undergraduates in his research, exposing them to basic science and teaching them practical skills such as computer coding and numerical analysis that will benefit them in STEM careers.

More technically, the first question Professor Royston will address is that of determining the leading contribution of virtual soliton-antisoliton pairs to processes involving perturbative particles. Through crossing symmetry in quantum field theory, such contributions are related to a soliton that emits or absorbs a high energy particle resulting in a large momentum transfer of order the mass of the soliton. Professor Royston will combine semiclassical techniques with a new tool --- the forced soliton equation --- to analyze this process. The forced soliton equation, discovered by Professor Royston and collaborators in 2020, is a wavelike equation that describes a soliton being driven along an arbitrarily specifiable trajectory. The second question Professor Royston will address concerns 'wall-crossing' phenomena for soliton bound-state spectra in certain supersymmetric gauge theories, and focuses on the manner in which wall-crossing can be understood from the semiclassical perspective of soliton field configurations and moduli spaces. In recent work, Professor Royston has noted a close connection between wall-crossing phenomena for magnetic monopoles and a construction in mathematics that aims to provide a compactification of monopole moduli space as a manifold with corners. Professor Royston, working in collaboration with a leading mathematician, aims to give a complete description of wall-crossing by analyzing the jumping behavior of zero-energy bound states in a certain quantum mechanics on monopole moduli space.

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.