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 charges. Finally, for D=4k+2 systems, we show 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. (C) 1997 Published by Elsevier Science B.V.