Anyons in one dimension

Particles possessing fractional statistics in two dimension have been dubbe d 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 f lux-tube attachment construction due to Wilczek. We will introduce a class of models describing 1D anyons, which has the great advantage over its 2D c ounterparts to be exactly solvable. The properties of these 1D anyons gener alize those of a Luttinger liquid and yield a complete classification of 1D fixed points when time-reversal symmetry is broken.