Boson-fermion equivalence by sugawara model

Abstract

The boson-fermion equivalence in 1(space)+1(time) dimension is discussed by original Abelian Sugawara model and its non-Abelian extension. Coleman and Mandelstam``s result are re-derived by using original Sugawara model. For the non-Abelian Boson-Fermion equivalence we construct the extended Sugawara model which contains a Wess-Zumino anomly. It is found that the space-space current commutation relation has a non-trivial anomaly. Also, Witten``s equivalence rule is obtained for anomaly coefficient N=1.