What is the Role of Torsion in the Universe?

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The effective action from the heterotic string compactification is studied on the manifolds with absolute parallelism. The cosmic string solutions resulting from the effective action are discussed in analogy with the dislocations in three-dimensional crystalline solid. The cosmic string density is concluded to be given by the torsion tensor of space-time, which gives rise to a compactification at least in one-dimensional direction in space-time. It is shown also the contorsion tensor defines the deficit angle. We have found a stringy solution in a six-dimensional model on M^4×T^2 which is compatible with that of Greene et al. and a cylindrically symmetric exact solution is obtained, which are different from the exact cosmic string solutions of the Einstein theory ever proposed. We have also obtained ar exact solution in a four-dimensional model on M^2×T^2 which can be considered as an example of the compactification on the noncompact Calabi-Yau manifold and may be expected to describe a space-time structure of our universe.
理論物理学刊行会の論文
1992-12-10

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