String Calculation of Fayet-iliopoulos D-terms in Arbitrary Supersymmetric Compactifications”

We calculate the Fayet-Iliopoulos D-terms generated at one loop for the heterotic string in any background which preserves four-dimensional space-time supersymmetry and maintains (2,0) world-sheet superconformal invariance. Although our calculation is performed in the full string theory, the result can be evaluated entirely in terms of properties of the massless spectrum. Furthermore it agrees with the result of a computation in the four-dimensional effective field theory using a stringy regularization. We also check our general result through a more explicit calculation in an orbifold background. Submitted to Nuclear Physics B x Work supported in part by the Department of Energy, contract DEAC03-76F00515 and the National Science Foundation, grant PHYS-83-10654 + Address after Sept. 1, 1987: Institute for Advanced Study, Princeton, NJ 08540.