Unification Theory by Superstring Model and Early Cosmology

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The project started in 1986 to study two fundamental questions of the string and/or the superstring: (a) whether the string theory can be qualified as a theory of unifying the space-time geometry and fundamental interactions of the matter, and (b) whether the string theory provides us with any reasonable universe.We first questioned ourselves why the string is used as amodel of unification theory and none others such as the membrane, etc.. For any model to be the candidate, it must generate zero-mass particles (gauge bosons and graveion) in its spectum. We calculated the Casimir energy of membrane and showed that it never generates massless particles if the space-time dimensions are integers. This is supposed to be true except for the string.For the string to be qualified as the unification theory, the field theory of string must be formulated in a way that is geometry independent. We studied the cubic action model of string which was suggested by Friedan, Yoneya and Witten, and then m … More athematically formulated by Hata, Itoh, Kygo, Kunitomo and Ogawa, and Horowitz, Lykken, Rhom and Strominger. By solving the equation of motion derived from the cubic action, we proved that all the conformal invariant background metric fields (including torsion and dilaton), which derived in the non-linear sigma model approach, are the classical solutions of the cubic action as well. This shows that the cubic action model is indeed a non-trivial and selfcontained geometry independent field theory of string.In order to extend above ideas to the superstring we studied a number of properties of superstring amplitudes. Polyakov's path integral method, which has been extensively used in the above arguments, was applied to superstrings and showed that the supermoduli and the conformal Killing spinor play fundamental roles in the gauge anomaly cancellation. These practices in superstring are indispendable in our next project where the geometry independent field theory of superstring is to be studied. Less