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We discuss the nature of criticality in the β2=2πN self-dual extension of the sine-Gordon model. This field theory is related to the two-dimensional classical XY model with a N-fold degenerate symmetry-breaking field. We briefly overview the already studied cases N=2,4 and analyze in detail the case N=3 where a single phase transition in the three-state Potts universality class is expected to occur. The Z3 infrared critical properties of the β2=6π self-dual sine-Gordon model are derived using two non-perturbative approaches. On one hand, we map the model onto an integrable deformation of the Z4 parafermion theory. The latter is known to flow to a massless Z3 infrared fixed point. Another route is based on the connection with a chirally asymmetric, su(2)4⊗su(2)1 Wess–Zumino–Novikov–Witten model with anisotropic current–current interaction, where we explore the existence of a decoupling (Toulouse) point. [Copyright &y& Elsevier]