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Anomalies and Fayet-Iliopoulos terms on warped orbifolds and large hierarchies

The anomalies in five-dimensional orbifold theories are examined in a generic type of non-factorizable geometries. In spite of complicated fermion wavefunctions, the shape of anomaly is found to be identical to that of flat theories. In particular it is split evenly on the orbifold fixed points. This result also follows from the arguments on the AdS/CFT correspondence and an anomaly cancellation mechanism. The cancellation with Chern-Simons term works if the four-dimensional effective theory is free from chiral anomalies. We also discuss the Fayet-Iliopoulos (FI) term in warped supersymmetric theories. Unlike the gauge anomaly, FI divergences reside not only on the orbifold fixed points but also in the whole five-dimensional bulk. The effect of the FI term is to generate supersymmetric masses for charged hypermultiplets, which are no longer constant but have metric factor dependence. We calculate the spectrum and wavefunctions of Kaluza-Klein modes in the presence of the FI term and discuss phenomenological implications to quark-lepton masses and large scale hierarchies.