Strong-weak coupling duality in four-dimensional string theory

We present several pieces of evidence for strong-weak coupling duality symmetry in the heterotic string theory, compactified on a six-dimensional torus. They include symmetry of the (1) low energy effective action, (2) allowed spectrum of electric and magnetic charges in the theory, (3) allowed mass spectrum of particles saturating the Bogomol'nyi bound, and (4) Yukawa couplings between massless neutral particles and massive charged particles saturating the Bogomol'nyi bound. This duality transformation exchanges the electrically charged elementary string excitations with the magnetically charged soliton states in the theory. It is shown that the existence of a strong-weak coupling duality symmetry in four-dimensional string theory makes definite predictions about the existence of new stable monopole and dyon states in the theory with specific degeneracies, including certain supersymmetric bound states of monopoles and dyons. The relationship between strong-weak coupling duality transformation in string theory and target space duality transformation in the five-brane theory is also discussed