Strong Coupling Fixed Points of Current Interactions and Disordered Fermions in 2D

The all-orders βeta function is used to study disordered Dirac fermions in 2D. The generic strong coupling fixed ‘points’ of anisotropic current-current interactions at large distances are actually isotropic manifolds corresponding to subalgebras of the maximal current algebra at short distances. The IR theories are current algebra cosets. We illustrate this with the simple example of anisotropic su(2), which is the physics of Kosterlitz-Thouless transitions, and find, among others, a line of fixed points and a fixed point corresponding to Zk parafermions. We work out the phase diagram for the Chalker-Coddington network model which is in the universality class of the integer Quantum Hall transition. We argue one phase has the fixed point osp(2|2)1/su(2)−1/2⊗u(1) and has promising exponents. Typeset using REVTEX ∗Laboratoire associé No. 280 au CNRS