Unconstrained off-shell N=3 supersymmetric Yang-Mills theory

Harmonic superspace is used to build up an unconstrained off-shell formulation of N=3 supersymmetry Yang-Mills theory. The theory is defined in an analytic N=3 superspace having M4(X)SU(3)/(U(1)(X)U(1)) as an even part. The basic objects are the analytic potentials which serve as gauge connections entering harmonic derivatives. The action is an integral over analytic superspace. The Lagrange density is surprisingly simple and it is gauge invariant up to total harmonic derivative. The equations of motion are integrability conditions on the internal space SU(3)/U(1)(X)U(1). It is the infinite set of auxiliary fields that allows the authors to overcome the 'N=3 barrier'.