GL(N, N) CURRENT-ALGEBRAS AND TOPOLOGICAL FIELD-THEORIES

The conformal field theory for the gl(N, N) affine Lie superalgebra in two space-time dimensions is studied. The energy-momentum tensor of t he model, with vanishing Virasoro anomaly, is constructed. This theory has a topological symmetry generated by operators of dimensions 1, 2 and 3, which are represented as normal-ordered products of gl(N, N) cu rrents. The topological algebra they satisfy is linear and differs fro m the one obtained by twisting the N = 2 superconformal models. It clo ses with a set of gl(N) bosonic and fermionic currents. The Wess-Zumin o-Witten model for the supergroup GL(N, N) provides an explicit realiz ation of this symmetry and can be used to obtain a free-field represen tation of the different generators. In this free-field representation, the theory decomposes into two uncoupled components with sl(N) and U( 1) symmetries. The non-abelian component is responsible for the extend ed character of the topological algebra, and it is shown to be equival ent to an SL(N)/SL(N) coset model. In the light of these results, the G/G coset models are interpreted as topological sigma models for the g roup manifold of G.