Dilaton, moduli and string/five-brane duality as seen from four dimensions

A naive dimensional reduction of the $N=1, D=10$ supergravity theory that naturally arises in five-brane models is used to determine the r\^ole of two fields which are basic ingredients of string models: the dilaton and, among the moduli, the breathing mode. It is shown that, under the duality transformation that relates five-branes and strings, these two fields exchange the r\^oles of 10-dimensional dilaton and radius of the compact manifold. A description of this phenomenon in terms of the linear multiplets of the 4-dimensional supergravity is also presented.