The Principal Investigator (PI) proposes to study certain problems in quantum field theory. He is planning further development of a weak-coupling method for the study of QCD in 2 + 1 dimensions. This method has made it possible to prove confinement in anisotropic weak-coupling QCD. The string tension in both spatial directions and the space-like Wilson loop have been evaluated for gauge group SU(2). He will also study of gauge orbit space in (3 + 1)-dimensional QCD. This concerns the Gribov problem in choosing a special set of coordinates and, perhaps more importantly, the further study of the non-compactness of gauge-theory orbit space. Finally he will study a new approach to string theory in which ten-dimensional strings naturally arise as extended objects in four-dimensional field theories. This may circumvent the need for compactification schemes and shed light on the AdS/CFT correspondence. The proposed research would be undertaken with the intention of sharing the results with others working in particle physics at large. The PI will supervise a graduate student who will work with him on some of these topics. The PI will also help coordinate collaborations within the City University system.
