On rotational excitations and axial deformations of BPS monopoles and Julia-Zee dyons

It is shown that Julia-Zee dyons do not admit slowly rotating excitations. This is achieved by investigating the complete set of stationary excitations which can give rise to nonvanishing angular momentum. The relevant zero modes are parametrized in a gauge invariant way and analyzed by means of a harmonic decomposition. Since general arguments show that the solutions to the linearized Bogomol'nyi equations cannot contribute to the angular momentum, the relevant modes are governed by a set of electric and a set of non-self-dual magnetic perturbation equations. The absence of axial dipole deformations is also established.

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