Strong–weak coupling duality in anisotropic current interactions

The recently proposed all orders β function for current interactions in two dimensions is further investigated. By using a strong–weak coupling duality of the β function, and some added topology of the space of couplings we are able to extend the flows to arbitrarily large or small scales. Using a nontrivial RG invariant we are able to identify sine-Gordon, sinh-Gordon and Kosterlitz–Thouless phases. We also find an additional phase with cyclic or roaming RG trajectories.