A Comment on Duality Transformations and (Discrete) Gauge Symmetries in Four-Dimensional Strings

Abstract

We discuss the relationship between target space modular invariance and discrete gauge symmetries in four-dimensional orbifold-like strings. First we derive the modular transformation properties of various string vertex operators of the massless string fields. Then we find that for supersymmetric compactifications the action of the duality elements, leaving invariant the multicritical points, corresponds to a combination of finite K\"ahler and gauge transformations. However, those finite gauge transformations are not elements of a remnant discrete gauge symmetry. We suggest that, at least in the case of Gepner models corresponding to tensor products of identical minimal models, the duality element leaving invariant the multicritical point corresponds to the ${\bf Z}_{k+2}$ symmetry of any of the minimal $N=2$ models appearing in the tensor product.