ABELIANIZATION OF SU(N) GAUGE-THEORY WITH GAUGE-INVARIANT DYNAMICAL VARIABLES AND MAGNETIC MONOPOLES

It is shown that SU(N) gauge theory coupled to adjoint Higgs can be ex plicitly re-written in terms of SU(N) gauge invariant dynamical variab les with local physical interactions. The resultant theory has a novel compact abelian U(1)((N-1)) gauge invariance. The above abelian gauge invariance is related to the adjoint Higgs field and not to the gauge group SU(N). In this abelianized version the magnetic monopoles carry ing the magnetic charges of (N-1) types have a natural origin and ther efore appear explicitly in the partition function as Dirac monopoles a long with their strings. The gauge invariant electric and magnetic cha rges with respect to U(1)((N-1)) gauge groups are shown to be vectors in root and co-root lattices of SU(N) respectively. Therefore, the Dir ac quantization condition corresponds to SU(N) Cartan matrix elements being integers, We also study the effect of the theta term in the abel ian version of the theory. (C) 1998 Published by Elsevier Science B.V.