Studying Special Holonomy Manifolds Using Conformal Field Theory Tools

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This award funds the research activities of Professor Daniel Robbins at the University at Albany. Conformal field theories (CFT's) are used in physics to describe phase transitions (such as ice melting into water), or to understand what happens in a quantum theory at very low or very high energies. CFT's also play a central role in string theory, which is the leading candidate for a quantum theory of gravity that unifies all of the fundamental forces of nature. Strings moving in different geometrical spaces are described by different CFT's that in turn lead to different physical phenomena and properties. This research program will explore the connections between CFT's, geometry, and the resulting physical laws. This work advances the national interest by fostering the progress of fundamental science at the interdisciplinary boundary between physics and mathematics, and thereby strengthening fundamental science within the United States. Students, both graduate and undergraduate, will also be involved in this project, receiving research training from Professor Robbins and receiving opportunities to present their work to other researchers.On a more technical level, this project will apply recently developed CFT techniques to a class of superconformal field theories (SCFT's) constructed from special holonomy manifolds. The philosophy and tools of the conformal bootstrap program and the modular bootstrap program, both of which exploit CFT consistency conditions in order to derive constraints on the defining data of a CFT, will be used to find constraints on the geometrical data of a class of manifolds that play an important role in string theory, and to explore aspects of their moduli spaces and the physical properties of the corresponding string theory constructions. The project will also apply recent ideas and tools from the study of CFT defects to the same class of SCFT's, investigating connections between theories connected by domain walls, boundary SCFT's, D-branes in the associated string theories, and the study of mathematical invariants of special holonomy manifolds.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.