WZW models of general simple groups Original Research Article

t is shown that a WZW model corresponding to a general simple group possesses in general different quantisations which are parametrised by Hom(π1(G), Hom(π1(G), U(1))). The quantum theories are generically neither monodromy nor modular invariant, but all the modular invariant theories of Felder et al. are contained among them. A formula for the transformation of the Sugawara expression for L0 under conjugation with respect to non-contractible loops in LG is derived. This formula is then used to analyse the monodromy properties of the various quantisations. It turns out that for π1(G) ⋟ ZN, with N even, there are two monodromy invariant theories, one of which is modular invariant, and for π1(G) ⋟ Z2 × Z2 there are eight monodromy invariant theories, two of which are modular invariant. A few specific examples are worked out in detail to illustrate the results.