Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-05-09
Nucl.Phys. B489 (1997) 603-625
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 20 pages, one figure. Version accepted for publication in Nuclear Physics B, minor corrections
Scientific paper
10.1016/S0550-3213(97)00014-X
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 reveals an osp(2/2)_1 affine symmetry at the pure critical point. A similar symmetry should hold at other fixed points. We apply methods of conformal field theory to determine the conformal weights at all levels. These weights can generically be negative because of non-unitarity. Constraints such as locality allow us to quantize the level k and the conformal dimensions. This provides a class of (possibly disordered) critical points in two spatial dimensions. Solving the Knizhnik-Zamolodchikov equations we obtain a set of four-point functions which exhibit a logarithmic dependence. These functions are related to logarithmic operators. We show how all such features have a natural setting in the superalgebra approach as long as gaussian disorder is concerned.
Maassarani Ziad
Serban Didina
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