PATH-INTEGRAL BOSONIZATION OF MASSIVE GNO FERMIONS

We show the quantum equivalence between certain symmetric space sine-G ordon models and the massive free fermions. In the massless limit, the se fermions reduce to the free fermions introduced by Goddard, Nahm an d Olive (GNO) in association with symmetric spaces K/G. A path integra l formulation is given in terms of the Wess-Zumino-Witten action where the field variable g takes value in the orthogonal, unitary, and symp lectic representations of the group G in the basis of the symmetric sp ace. We show that, for example, such a path integral bosonization is p ossible when the symmetric spaces K/G are SU(N) x SU(N)/SU(N); N less than or equal to 3, Sp(2)/U(2) or SO(8)/U(4). We also address the rela tion between massive GNO fermions and the non-Abelian solitons, and ex plain the restriction imposed on the fermion mass matrix due to the in tegrability of the bosonic model. (C) 1997 Elsevier Science B.V.