Nonperturbative formulation of superstring theory

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(1) Space-time uncertainty principle : More than ten years ago, Yoneya has proposed a simple uncertainty relation, which restricts the shortest observable distance scales in space-time, as a qualitative characterization of the resolution of the ultraviolet problems of quantum gravity in string theory. During the present project, this principle was further clarified and developed by Yoneya. The characteristic length scales of string theory, in particular, the role of the M-theory scale, gィイD31/3(/)sィエD3lィイD2sィエD2, can now be explained on the basis of this principle. (2) D-branes : We have investigated a variety of different aspects of the dynamics of D-branes which are presently believed to be one of the key features for the nonperturbative string/M theory. Kato gave a formulation of D-branes in curved space-time and studied T-dualities on the basis of the automorphisms of the conserved currents. Kazama constructed a general path-integral formalism for studying the interactions of D-bra … More nes and strings. Jevicki and Yoneya, and, later, Jevicki, Kazama and Yoneya studied the role of (generalized) conformal symmetries for D-branes. We showed that the generalized conformal symmetry in conjunction of the constraint coming from supersymmetry is useful for extracting the dynamics of D-branes in the eikonal approximation. Yoneya studied the multi-body interactions of D-particles, and showed that the supersymmetry Yang-Mills matrix quantum mechanics precisely reproduces the first nonlinear effect described by the supergravity in 11 dimensions. Yoneya analyzed the condition for the validity of the AdS/CFT correspondence in Matrix theory and obtained the first results for the correlation functions in the large N limit which exhibit some interesting behavior, suggesting a screening mechanism which may reconcile the holographic behavior of the matrix theory with Lorentz invariance. Kazama extended the, previous work by Jevicki, Kazama and Yoneya on the role of generalized conformal symmetry in the dynamics of D-branes by taking account the supersymmetry more precisely without making the eikonal approximation and succeeded to derive the supersymmetric Ward identity. In studying the symmetry structure for systems with unstable D-branes, Yoneya showed that such systems have N=2 space-time supersymmetry in a spontaneously broken phase. These more recent works should shed new light on the symmetry structure of string theories and are hoped to be a useful basis for further development of our program toward the nonperturbative formulation of the theory. (3) Noncommutative structure : Kato investigated the structure of spacetime and degrees of freedom in string theory from the viewpoint of noncommutative geometry. Especially, the duality relation between the noncommutativity in the world volume and that of the target spacetime was clarified by constructing the boundary state with full noncommutativity which describes the interaction of string with D-brane. Also it is under study in what mechanism the noncommutativity by the background B-field appears in the non-local point particle theory whose equivalence to the open string theory was shown before. Ultimately, the studies on noncommutative structure are expected to be related to Yoneya's space-time uncertainty principle. Yoneya's recent investigation along such a direction suggests that will be indeed the case. Less