EXACT DUALITY SYMMETRIES IN CFT AND STRING THEORY

The duality symmetries of WZW and coset models are discussed. The exac t underlying symmetry responsible for semiclassical duality is identif ied with the symmetry under affine Weyl transformations. This identifi cation unifies the treatment of duality symmetries and shows that in t he compact and unitary case they are ''act symmetries of string theory to all orders in alpha' and in the string coupling constant. Non-comp act WZW models and cosets are also discussed. A toy model is analyzed suggesting that duality can survive as an exact symmetry.