RUI: Supersymmetric Gauge Theory and String Theory

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This award funds the research activities of Professor Naculich at Bowdoin College, an undergraduate institution located in Brunswick, Maine. This research is part of an on-going effort by the worldwide community of theoretical elementary particle physicists to develop mathematical models to explain the nature and behavior of the smallest constituents of matter (elementary particles). More specifically, this research aims at developing more efficient mathematical tools for calculating the predictions of existing models of quarks and gluons called "gauge theories". A second goal of this research is to explore links between gauge theories on the one hand, and theories (such as supergravity and string theory) that describe the behavior of gravitons, the particles responsible for the force of gravity, on the other. The insights gained through this research will be disseminated through journal publications, seminars, and conference proceedings. This research also integrally involves participation by undergraduates, and will therefore contribute to their education by providing hands-on training in research methods in theoretical physics, as well as exposure to quantum mechanics, group theory, and quantum field theory. Such involvement will encourage and prepare highly-talented students for graduate study and careers in scientific fields.In more technical terms, this project focuses on both perturbative and non-perturbative aspects of supersymmetric gauge theory and supergravity theory, as illuminated by their connection to string theory. In particular, this research will explore constraints among tree-level and loop-level gauge theory scattering amplitudes that are generic to gauge theory, independent of the matter content of the theory. These include both constraints that depend only on the gauge group, as well as Bern-Carrasco-Johansson type relations. The research will further investigate the structure of loop-level SU(N) gauge theory amplitudes that are subleading in the 1/N expansion, their infrared divergences, and potential iterative structures among these amplitudes. Finally, the project will study the structure of the amplitudes of supergravity, their infrared divergences, and potential relations between supergravity and supersymmetric Yang-Mills amplitudes at the loop level.