Towards Abelian-like formulation of the dual gluodynamics

We consider gluodynamics in case when both color and magnetic charges are p resent. We discuss First short distance physics, where only the fundamental /Q(m)/ = 1 monopoles introduced via the 't Hooft loop can be considered co nsistently. We show that at short distances the external monopoles interact as pure Abelian objects. This result can be reproduced by a Zwanziger-type Lagrangian with an Abelian dual gluon and ordinary gluons in an adjoint re presentation. We introduce also an effective dual gluodynamics which might be a valid approximation at distances where the monopoles /Q(m)/ = 2 can be considered as point-like as well. Assuming the monopole condensation we ar rive at a model which is reminiscent in some respect of the Abelian Higgs m odel but, unlike the latter leaves space for the Casimir scaling. (C) 2001 Elsevier Science B.V. All rights reserved.