Generalized Chern-Simons Terms and Chiral Anomalies in N=1 Supersymmetry

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The gauging of axionic, Stueckelberg-type, shift symmetries with generalized Chern-Simons terms and the Green-Schwarz mechanism of anomaly cancellation has recently been studied in the context of certain string compactifications and with regard to the phenomenology of unusual variants of Z'-bosons. In this talk, following recent work with De Rydt, Rosseel, Schmidt and Van Proeyen, I summarize how such theories can be reconciled with global and local N=1 supersymmetry. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups.
6 pages, Latex2e. Prepared for the Proceedings of the VII. International Workshop "Lie Theory and its Applications to Physics", 18 - 24 June 2007, Varna. v2: references added

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