Criticality in self-dual sine-Gordon models

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