Scattering of gauge and higgs fields by self-dual monopoles

The hidden symmetries of multi-centre metrics

“…(8.17) in this case. Since there already exists an extensive discussion of the resulting solution in the literature [33] we shall not pursue this matter further here.…”

Applications of chiral supersymmetry for spin fields in self-dual backgrounds

“…The latter result throws a new light on the well-known fact [10,9,3,4] that the ω = 0 eigenfluctuations can be expressed in terms of the eigenfunctions of either D or D 2 . The starting point is the usual 4-dimensional Euclidean DYM operator in the chiral (supersymmetric) basis, namely,…”

“…provides us with four orthogonal fluctuation eigenmodes. (From the explicit expressions of the 't Hooft matrices one sees that (δA µ ) (4) is a gauge mode, and the other three satisfy the transversality condition.) Formula (4.6) is known [9,10], but we thought it worth pointing out that it is a manifestation of the purely vectorial supersymmetry (4.4)-(4.5) and that the latter is just the m = 1 2 special case in the series of supersymmetries (4.2)-(4.3).…”

“…The bound state problem in this background has been extensively investigated before [3] for an isospin 1 particle on the basis of the Jackiw-Rebbi [6] angular momentum analysis of D (see also ref. [4]). If we exclude the zero modes then, according to the arguments given above, it is sufficient to study the scalar Laplacian D 2 , and for the gauge potential (2.1), this Laplacian (for x 4 -independent wave-functions) is easily computed to be…”

“…The purpose of the present paper is to show how the reduction can be used to simplify and clarify some recent work on the discrete spectra and symmetries of self-dual DYM operators. We first show how the discrete eigenvector system (apart from the zero modes) and the symmetries of D may be reconstructed from those of D 2 , and then use D 2 to (i) simplify and generalize to any isospin the previous analyses [3,4] of the (nonzero mode) spectrum of the DYM operator of a Bogomolny-Prasad-Sommerfield (BPS) monopole [5] (the zero-modes have been completely analyzed in Refs. [6] and [7]), (ii) explain the remarkable but complicated 'dynamical' Kepler and supersymmetries of the self-dual D 2 found recently by D'Hoker and Vinet [8],…”