The Linear Multiplet and Quantum 4-D String Effective Actions

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.