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

Abstract

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. In particular the mass formula for BPS states is given by the periods of a special differential on this surface. In this note we point out that the surface 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 implies that these monopoles are related to the 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.

uuencoded latex, 15 pages, 1 figure. To appear in Physics Letters B

References in corpus (4)

• Integrable systems and supersymmetric gauge theory
• Monopole Scattering with a Twist
• Monopole Zeros
• Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold

Cited by in corpus (15)

• Three Dimensional Gauge Theories and Monopoles
• BPS Monopoles
• Multiscale N=2 SUSY field theories, integrable systems and their stringy/brane origin -- I
• Branes and integrability in the N=2 SUSY YM theory
• Cyclic Monopoles
• On the tetrahedrally symmetric monopole
• Cyclic Monopoles, Affine Toda and Spectral Curves
• Integrability of BPS equations in ABJM theory
• $A_n^{(1)}$ Toda solitons and the dressing symmetry
• Cyclic Calorons
• Higher charge periodic monopoles
• Construction of Nahm data and BPS monopoles with continuous symmetries
• Towards a Classification of Charge-3 Monopoles with Symmetry
• Hyperbolic monopole data
• Dualities in integrable systems and N=2 theories