Is the String Coupling Constant invariant under T-duality?

It is well known that under T-duality the sigma model dilaton (which is normally thought to be related to the string coupling constant through the simple formula $\kappa = exp <\phi >$), undergoes an additive shift. On the other hand, Kugo and Zwiebach, using a simplified form of string field theory, claim that the string coupling constant does not change under the T-duality. Obviously, what seems to happen is that two different coupling constants, associated to different dilatons, are used. In this contribution we shall try to clarify this, and related issues.