Seiberg-Witten theory, monopole spectral curves and affine Toda solitons

Using Seiberg-Witten theory it is known that the dynamics of N = 2 supersymmetric SU(n) Yang-Mills theory is determined by a Riemann surface Σn. In particular the mass formula for BPS states is given by the periods of a special differential on Σn. In this note we point out that the surface Σn can be obtained from the quotient of a symmetric n-monopole spectral curve by its symmetry group. Known results about the Seiberg-Witten curves then imply that these monopoles are related to the An−1(1) Toda lattice. We make this relation explicit via the ADHMN construction. Furthermore, in the simplest case, that of two SU(2) monopoles, we find that the general two monopole solution is generated by an affine Toda soliton solution of the imaginary coupled theory.