BKT phase transitions in two-dimensional systems with internal symmetries

The Berezinsky-Kosterlitz-Thouless (BKT) type phase transitions in two-dimensional systems with internal abelian continuous symmetries are investigated. The necessary conditions for they can take place are: 1) conformal invariance of the kinetic part of the model action, 2) vacuum manifold must be degenerated with abelian discrete homotopy group pi_1. Then topological excitations have a logarithmically divergent energy and they can be described by effective field theories generalizing the two-dimensional euclidean sine-Gordon theory, which is an effective theory of the initial XY-model. In particular, the effective actions for the two-dimensional chiral models on maximal abelian tori T_G of simple compact groups G are found. Critical properties of possible effective theories are determined and it is shown that they are characterized by the Coxeter number h_G of lattices from the series A,D,E,Z and can be interpreted as those of conformal field theories with integer central charge C=n, where n is a rank of the groups pi_1 and G. A possibility of restoration of full symmetry group G in massive phase is also dicussed.