Collaborative Research: Investigations on Fluids, Gauge Fields, Matrix Models and Gravity

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This Collaborative award funds the research activities of Professors V.P. Nair and A.P. Polychronakos at the City College of the City University of New York, and Professor Daniel Kabat at Lehman College of the City University of New York.Physics made tremendous strides during the 20th century, with the landmark achievements of general relativity, relevant to the universe at large, and quantum theory, relevant to the microscopic structure of matter. Further progress calls for studying situations in which our understanding of these theories is incomplete. The interior of a black hole and the binding of quarks to form atomic nuclei are two examples of poorly understood situations. This research program brings powerful mathematical tools to bear on these and related problems. As a result, research in this area advances the national interest by promoting the progress of science in one of its most fundamental directions: the discovery and understanding of new physical laws. Moreover, this research will involve graduate and undergraduate students, providing ideal training for the next generation of scientists and science educators. By running a joint program between City College and Lehman College we achieve a critical mass and can draw on a large pool of students, especially from minority and under-represented groups which are a large part of the student body at both colleges.More technically, this project furthers an investigation into a new formulation of fluid dynamics focusing on symmetry structures. It elaborates on previously initiated techniques to study gauge theories in 2+1 dimensions and their extension to the realistic case of four dimensions. New calculational techniques, developed by Professors Kabat, Nair and others, will be used to explore the effects of spin and novel boundary conditions on the Casimir force. Various aspects of field theory on "fuzzy" (noncommutative) spaces will be explored using recently developed techniques, the eventual goal being an effective action which captures nonperturbative effects in the large-N (continuum) limit. Finally the AdS/CFT (Anti-de Sitter Space/Conformal Field Theory) correspondence will be used as a precise formulation of quantum gravity to investigate how local bulk physics emerges from the CFT. Previous work by Kabat and collaborators, relying on 1/N perturbation theory to represent local bulk observables in the CFT, will be extended to higher orders in 1/N and used to constrain CFT four-point functions. The entanglement structure of the CFT will be used to study the black hole interior, and the failure of bulk locality at finite N for black holes and cosmology will be investigated.