One-dimensional flows in the quantum Hall system

We construct the c function whose gradient determines the RG flow of the conductivities (ifσxy and σxx) for a quantum Hall system, subject to two assumptions. (1) We take the flow to be invariant with respect to the infinite discrete symmetry group, ΓH, recently proposed by several workers to explain the ‘superuniversality’ of the delocalization exponents in these systems. (2) We also suppose the flow to be ‘quasi-holomorphic’ (which we make …