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 excitations of a gas of spinless interacting fermions on a circle in the gapless regime (Luttinger liquid) is investigated. Functional techniques and modular-transformation properties are used to compute all correlation functions for a finite size and temperature. Forward-scattering disorder is treated exactly. Laughlin experiments on charge transport in a quantum Hall fluid on a cylinder are reviewed in this CFT framework. Edge excitations above a given bulk excitation are described by a twisted version of the Luttinger effective theory. Luttinger CFTs corresponding to the $\nu=1/(2p+1)$ filling fractions are rational CFTs (RCFT). Generators of the extended symmetry algebra are identified as edge-fermion creators and annihilators, thus giving a physical meaning to the RCFT viewpoint on edge excitations of these sequences.