NONUNITARY CONFORMAL FIELD-THEORY AND LOGARITHMIC OPERATORS FOR DISORDERED-SYSTEMS

We consider the supersymmetric approach to Gaussian disordered systems like the random bond Ising model and Dirac model with random mass and random potential. These models appeared in particular in the study of the integer quantum Hall transition. The supersymmetric approach reve als an osp(2/2)(1) affine symmetry at the pure critical point. A simil ar symmetry should hold at other fixed points. We apply methods of con formal field theory to determine the conformal weights at all levels. These weights can generically be negative because of non-unitarity. Co nstraints such as locality allow us to quantize the level k and the co nformal dimensions. This provides a class of (possibly disordered) cri tical points in two spatial dimensions. Solving the Knizhnik-Zamolodch ikov equations we obtain a set of four-point functions which exhibit a logarithmic dependence. These functions are related to logarithmic op erators. We show how all such features have a natural setting in the s uperalgebra approach as long as Gaussian disorder is concerned. (C) 19 97 Elsevier Science B.V.