Duality, self-duality, sources and charge quantization in abelian N-form theories

We investigate duality properties of N-form fields, provide a symmetric way of coupling them to electric/magnetic sources, and check that these charges obey the appropriate quantization requirements. First, we contrast the D = 4k case, in which duality is a well-defined SO(2) rotation generated by a Chern-Simons form leaving the action invariant, and D = 4k + 2 where the corresponding ostensibly SO(1, 1) rotation is not only not an invariance but does not even have a generator. When charged sources are included we show explicitly in the Maxwell case how the usual Dirac quantization arises in a fully symmetric approach attaching strings to both types of changes. Finally, for D = 4k + 2 systems, we show how charges can be introduced for self-dual (2k)-forms, and obtain the D = 4k models with sources by dimensional reduction, tracing their duality invariance to a partial invariance in the higher dimensions.