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We explore general properties of matter coupled supergravities with antisymmetric tensor fields embedded in linear multiplets. The four-dimensional supersymmetric version of the Green-Schwarz mechanism leads to the introduction of super Chern-Simons form multiplets whose general component expressions are derived. The use of superconformal techniques allows us to discuss several topics relevant to superstring effective actions and in particular to give simple forms for the string-loop corrections to the Kahler potential and the U(1) anomaly cancelling term present in certain superstring compactifications.
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Cecotti et al. (1987) studied this question.
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