Anomaly cancelation in field theory and F-theory on a circle

We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional kaluza-klein theory obtained after circle compactification. we identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the coulomb branch. the maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced chern-simons terms in the three- and five-dimensional effective theory. the arising symmetries are argued to play a key role in the study of the m-theory to f-theory limit on calabi-yau manifolds. for example, using the fact that all fully resolved f-theory geometries inducing multiple abelian gauge groups or non-abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure abelian or pure non-abelian anomalies in these models.