  In 4-D heterotic superstrings, the dilaton and antisymmetric tensor fields
belong to a linear N=1 supersymmetric multiplet L. We study the lagrangian
describing the coupling of one linear multiplet to chiral and gauge multiplets
in global and local supersymmetry, with particular emphasis on string
tree-level and loop-corrected effective actions. This theory is dual to an
equivalent one with chiral multiplets only. But the formulation with a linear
multiplet appears to have decisive advantages beyond string tree-level since,
in particular, <L> is the string loop-counting parameter and the duality
transformation is in general not exactly solvable beyond tree-level. This
formulation allows us to easily deduce some powerful non-renormalization
theorems in the effective theory and to obtain explicitly some loop corrections
to the string effective supergravity for simple compactifications. Finally, we
discuss the issue of supersymmetry breaking by gaugino condensation using this
formalism.
