Abstract
In this paper the compactification of ten-dimensional superstring theories over homogeneous coset spaces S/R is analyzed. We construct explicitly the Ricci-flattening spin connection with torsion for the non-symmetric spaces G 2/SU(3), SU(3)/U(1) × U(1) and Sp(4)/SU(2) × U(1). These spaces provide a solution to the classical field equations with vanishing energy-momentum tensor and therefore one might expect that the conformal invariance of the string theory is preserved. We discuss the two-dimensional non-linear σ-model with Wess-Zumino term corresponding to the homogeneous spaces S/R. In addition, we investigate the constraints for the compactification coming from the requirement of unbroken supersymmetry and anomaly cancellation and give explicit examples of consistent compactification with S and R being embedded into the ten-dimensional gauge group E 8.
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