Abstract
The heterotic superstring is considered in a fixed background space-time with torsion. Conditions on the background fields from requiring finiteness, conformal invariance, anomally cancellation and unbroken supersymmetry are derived and compared. Consistency between these conditions fixes an ambiguity in the torsion Bianchi identity. Spaces satisfying all these requirements (at least to lowest order), with non-zero torsion and that compactify to four dimensions with N = 1 supersymmetry, are discussed and higher order corrections are briefly considered. There is a “triality” relation between world-sheet and space-time supersymmetries in such spaces.
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