DUALITY, SELF-DUALITY, SOURCES AND CHARGE QUANTIZATION IN ABELIAN N-FORM THEORIES

We investigate duality properties of N-form fields, provide a symmetri c way of coupling them to electric/magnetic sources, and check that th ese charges obey the appropriate quantization requirements, First, we contrast the D=4k case, in which duality is a well-defined SO(2) rotat ion generated by a Chern-Simons form leaving the action invariant, and D=4k+2 where the corresponding ostensibly SO(1,1) rotation is not onl y not an invariance but does not even have a generator. When charged s ources are included we show explicitly in the Maxwell case how the usu al Dirac quantization arises in a fully symmetric approach attaching s trings 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 wit h sources by dimensional reduction, tracing their duality invariance t o a partial invariance in the higher dimensions. (C) 1997 Published by Elsevier Science B.V.