Space-Time Independent Formulation of String Theories

点击翻译按钮获取中文摘要

We have started our research for constructing the unified theory of fundanmental interactions of elementary particles including gravity on the basis of string theories. Our aim is, in particular, to look for the string theory formulation in such a way that the theory does not depend on a particular background space-time geometry. For this purpose we have set forth with concrete problems. Namely, we clarified mathematically complicated aspects of string theories left untouched so far, gained deep insights into the vacuum structures in the early universe, and tried to extend the stringy symmetries to the off-mass-shell. Let us survey what we have achieved.1. We analyzed the mechanism of cancellation of the Lorentz anomaly known in the light-cone string field theory. By using the methods of S-matrix approach. And of path integral formalism.2. we clarified mathematically complicated features of the PHI^3 theory, which has been put forward as a geometry independent formulation. In particula … More r, we proved the invariance under the general coordinate transformation by using the mid-point time prescription.3. Going back to the original Einstein theory of gravity. We tackled the phase transition problem accompanied by topology change caused by gravitational instantons with no tunneling barrier. This study is expected to serve to scrutinize the vacuum structures in the early universe. We advocated the usefulness of the Born-Oppenheimer method which is supposed to replace the semi-classical approximation .4. To grasp the connection between the two approaches based on the path integral method and the string field theory. We investigated the concept of "string emission vertex operator" . It has been proved that the requirement of the Weyl invariance the vertex in the first approach is equivalent to the classical equation of motion in the latter. The implications of the BRST symmetry in the field theory approach is investigated in terms of the actual off-shell scattering amplitudes in the path integral approach.5. A physical interpretation was given of the Virasoro algebra discovered in the two-dimensional matrix models of gravity. Our interpretation is referred to the continuum non-critical string theory.6. As a byproduct of our research. There is a paper on the algebraic extension of two-dimensional quantum chromodynamics. There is also a comprehensive review article on the light-cone gauge string field theory. Less