Outstanding Junior Investigator Program: Progress report for the period ending December 31, 1988

Since the submission of the last proposal for the Outstanding Junior Investigator Program in January 1988, research has entailed: an investigation of the nonperturbative geometry of string theory and loop space; a paper on the relation between nonlinear sigma models (with nonabelian topological interactions) and the Hubbard model, with application to high-temperature superconductivity; completion of the calculation of the Ricci curvature of DiffS1/SL(2,R); the determination that the low energy limit of closed string theory follows from the symplectic geometry of loop space; the demonstration that in a theory of gravity coupled to second rank antisymmetric tensor field there exist black holes with axionic charge. This charge can be measured by an interference experiment if a beam of strings (or particles if string theory is correct) passes through the black hole. The result is a generalization of the Bohm-Aharanov effect to second rank antisymmetric tensor fields. In this paper is a summary of this work together with last year's work. 46 refs