Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold

Abstract

We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah-Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole dynamics to be translated into results about the dynamics of 3-monopoles. Using a numerical ADHMN construction we compute the monopole energy density at various points on two interesting geodesics. The first is a geodesic over the two-dimensional rounded cone submanifold corresponding to right angle scattering and the second is a closed geodesic for three orbiting monopoles.

latex, 22 pages, 2 figures. To appear in Nonlinearity

References in corpus (5)

• The Moduli Space Metric for Well Separated BPS Monoples
• Symetric Monopoles
• Symmetric Monopoles
• Quantising the B=2 and B=3 Skyrmion systems
• The moduli space metric for tetrahedrally symmetric 4-monopoles

Cited by in corpus (11)

• Rational Maps, Monopoles and Skyrmions
• BPS Monopoles
• Instantons, Three Dimensional Gauge Theories and Monopole Moduli Spaces
• A note on the (1, 1,..., 1) monopole metric
• Seiberg-Witten theory, monopole spectral curves and affine Toda solitons
• New hyper-Kaehler manifolds by fixing monopoles
• SU(N) Monopoles and Platonic Symmetry
• Symmetric hyperbolic monopoles
• A Monopole Metric
• Bound monopoles in the presence of a dilaton
• Towards a Classification of Charge-3 Monopoles with Symmetry