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We analyse the proposal of sliding phases (SP) in layers hosting global U(1)symmetric variables with finite inter-layer Josephson coupling. Based on theKosterlitz-Thouless renormalization group (RG) approach, such phases werepredicted to exist in various layered (or 1D quantum coupled) systems. The keyin the RG argument is treating the coupling as though the variables arenon-compact. Large scale Monte Carlo simulations of a layered model, where theSP is supposed to exist, finds no indication of such a phase. Instead, 3Dbehavior is observed. This result is consistent with the asymptotically exactanalytical solution. A generic argument against SP in translationally invariantsystems with short range interactions is provided. We have also suggested analternative model for the SP -- adding long-range interactions to theinter-layer Josephson term.

Sliding phases in U(1) symmetric systems -- mirage of the renormalization group