Abstract
Criteria for unbroken N = 1 space-time supersymmetry in the heterotic string theory in the presence of background fields are discussed. We make use of the construction of the fermion vertex operator in the Neveu-Schwarz-Ramond model. (2,0) world-sheet supersymmetry is shown to be one of the necessary conditions for space-time supersymmetry in most cases. Constraints on the various background fields implied by (2,0) world-sheet supersymmetry are derived, taking into account the effect of σ-model loop corrections. Special care is taken to study the effect of local Lorentz and gauge anomaly on these constraints. Our analysis determines the constraints unambiguously up to field redefinitions.
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