BPS Saturated and Non-Extreme States in Abelian Kaluza-Klein Theory and Effective N=4 Supersymmetric String Vacua

We summarize results for all four-dimensional Bogomol'nyi-Sommerfield-Prasat (BPS) saturated and non-extreme solutions of the ($4+n$)-dimensional Abelian Kaluza-Klein theory. Within effective N=4 supersymmetric string vacua, parameterized in terms of fields of the heterotic string on a six-torus, we then present a class of BPS saturated states and the corresponding non-extreme solutions, specified by $O(6,22,Z)$ and $SL(2,Z)$ orbits of general dyonic charge configurations with zero axion. The BPS saturated states with non-negative $O(6,22,Z)$ norms for electric and magnetic charge vectors, along with the corresponding set of non-extreme solutions, are regular with non-zero masses. BPS saturated states with the negative charge norms are singular, unaccompanied by non-extreme solutions and become massless at particular points of the moduli space. The role that such massless states may play in the enhancement of non-Abelian gauge symmetry as well as local supersymmetry is addressed.