Lines generated by marginal deformations of WZW models are considered. The Weyl symmetry at the WZW point implies the existence of a duality symmetry on such lines. The duality is interpreted as a broken gauge symmetry in string theory. It is shown that at the two end points the axial and vector cosets are obtained. This shows that the axial and vector cosets are equivalent CFTs both in the compact and the non-compact cases. Moreover, it is shown that there are σ-model deformations that interpolate smoothly between manifolds with different topologies.
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We thank S. Elitzur, C. Kounnas, A. Polychronakos, E. Rabinovici, M. Roëek and A. Shapere for discussions. We also thank C. Kounnas and M. Ro~ekfor useful comments on the paper. AG would like to thank the Institute for theoretical Physics at Santa Barbara where this work was completed. EK would like to thank the Tel Aviv University and especially the Hebrew University in Jerusalem for their warm hospitality while this work was done. This work was supported in part by NSF grant No. PHY89-04035. We would also like to thank the referee for prompting us to make our arguments clearer.