  We have devised a general scheme that provides exact results for the scaling
dimensions of all allowed in multi-channel Luttinger Liquids local
perturbations. The technique developed provides universal description and
establishes relations between scaling dimensions of perturbations in different
phases of Luttinger Liquid. These multiple relations between scaling dimensions
are universal. They are valid for all Luttinger Liquids with arbitrary
current-current and density-density interactions. We have also established
duality transformation between different subsets of Luttinger Liquid phases
known for single-channel liquid as duality between weak link and weak scatterer
limits.
