Magnetic Monopoles, Bogomol'nyi Bound and SL(2,Z) Invariance in String Theory

We show that in heterotic string theory compactified on a six dimensional torus, the lower bound (Bogomol'nyi bound) on the dyon mass is invariant under the SL(2,Z) transformation that interchanges strong and weak coupling limits of the theory. Elementary string excitations are also shown to satisfy this lower bound. Finally, we identify specific monopole solutions that are related via the strong-weak coupling duality transformation to some of the elementary particles saturating the Bogomol'nyi bound, and these monopoles are shown to have the same mass and degeneracy of states as the corresponding elementary particles.