Renormalization group for network models of Quantum Hall transitions

We analyze in detail the renormalization group flows which follow from the recently proposed all orders beta functions for the Chalker-Coddington network model. The flows in the physical regime reach a true singularity after a finite scale transformation. Other flows are regular and we identify the asymptotic directions. One direction is in the same universality class as the disordered XY model. The all orders beta function is computed for the network model of the spin Quantum Hall transition and the flows are shown to have similar properties. It is argued that fixed points of general current-current interactions in 2d should correspond to solutions of the Virasoro master equation. Based on this we identify two coset conformal field theories osp(2N|2N)_1 /u(1)_0 and osp(4N|4N)_1/su(2)_0 as possible fixed points and study the resulting multifractal properties. We also obtain a scaling relation between the typical amplitude exponent alpha_0 and the typical point contact conductance exponent X_t which is expected to hold when the density of states is constant.