A field theory with generalized statistics in one space dimension is introduced. The statistics enters the scene through the coupling of the matter fields to a statistical gauge field, as it happens in the Chern-Simons theory in two dimensions. We study the particle-hole excitations and show that the long wavelength physics of this model describes a gas obeying the Haldane generalized exclusion statistics. The statistical interaction is found to provide a way to describe the low-T critical properties of one-dimensional non-Fermi-liquids.
Particles possessing fractional statistics in two dimension have been dubbed anyons. We want to show how it is possible to extend this concept in the case of conformally invariant systems in one dimension, and reproduce the flux-tube attachment construction due to Wilczek. We will introduce a class of models describing 1D anyons, which has the great advantage over its 2D counterparts to be exactly solvable. The properties of these 1D anyons generalize those of a Luttinger liquid and yield a complete classification of 1D fixed points when time-reversal symmetry is broken. I HOW ANYONS MAY ARISE IN ONE DIMENSION Fractional statistics arises in two dimensions because the exchange of particle is encoded by the braid group BN rather than by the permutation group S N. This fractional exchange statistics is often thought to be possible only in two dimensions in contrast with for instance fractional exclusion statistics which is defined independently of the dimensionality. However already in their seminal paper Leinaas and hfyrheim investigated the possibility to define intermediate statistics in one dimension by considering generalized boundary conditions for wavefunctions