Criticality in self-dual sine-Gordon models

We discuss the nature of criticality in the beta(2) = 2piN 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 Z(3) infrared critical properties of the beta(2) = 6pi 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 Z(4) parafermion theory. The latter is known to flow to a massless Z(3) infrared fixed point. Another route is based on the connection with a chirally asymmetric, su(2)(4) circle times su(2)(1) Wess-Zumino-Novikov-Witten model with anisotropic current-current interaction, where we explore the existence of a decoupling (Toulouse) point. (C) 2002 Elsevier Science B.V. All rights reserved.