WZW MODELS OF GENERAL SIMPLE-GROUPS

It is shown that a WZW model corresponding to a general simple group p ossesses in general different quantisations which are parametrised by Hom(pi(1)(G), Hom(pi(1)(G), U(1))). The quantum theories are generical ly neither monodromy nor modular invariant, but all the modular invari ant theories of Felder et al. are contained among them. A formula for the transformation of the Sugawara expression for L(0) under conjugati on with respect to non-contractible loops in LG is derived. This formu la is then used to analyse the monodromy properties of the various qua ntisations. It turns out that for pi(1)(G) congruent to Z(N), With N e ven, there are two monodromy invariant theories, one of which is modul ar invariant, and for pi(1)(G) congruent to Z(2) x Z(2) there are eigh t monodromy invariant theories, two of which are modular invariant. A few specific examples are worked out in detail to illustrate the resul ts.