Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of nu=1/(2p+1) quantum Hall sequences

An effective conformal field theory (CFT) describing the low-energy excitat ions of a gas of spinless interacting fermions on a circle in the gapless r egime (Luttinger liquid) is investigated. Functional techniques and modular -transformation properties are used to compute all correlation functions fo r a finite size and temperature. Forward-scattering disorder is treated exa ctly. Laughlin experiments on charge transport in a quantum Hall fluid on a cylinder are reviewed in this CFT framework. Edge excitations above a give n bulk excitation are described by a twisted version of the Luttinger effec tive theory. Luttinger CFTs corresponding to the nu = 1/(2p + 1) filling fr actions are rational CFTs (RCFT). Generators of the extended symmetry algeb ra are identified as edge-fermion creators and annihilators, thus giving a physical meaning to the RCFT viewpoint on edge excitations of these sequenc es.