Monopole-charge instability

Details Monopole-charge instability Monopole-charge instability

2009-09-14

arxiv.org/abs/0909.2523v3

Int.J.Mod.Phys.A3:665-702,1988

Physics

High Energy Physics

High Energy Physics - Theory

LaTex, 38 pages. 7 figures and 2 photos. Posted for the record. Originally published 20 years ago, with Note added in 2009: Ho

Scientific paper

10.1142/S0217751X88000291

For monopoles with nonvanishing Higgs potential it is shown that with respect to "Brandt-Neri-Coleman type" variations (a) the stability problem reduces to that of a pure gauge theory on the two-sphere (b) each topological sector admits one, and only one, stable monopole charge, and (c) each unstable monopole admits $2\sum_{q<0} (2|q|-1)$ negative modes, where the sum goes over all negative eigenvalues $q$ of the non-Abelian charge $Q$. An explicit construction for (i) the unique stable charge (ii) the negative modes and (iii) the spectrum of the Hessian, on the 2-sphere, is then given. The relation to loops in the residual group is explained. The negative modes are tangent to suitable energy-reducing two-spheres. The general theory is illustrated for the little groups U(2), U(3), SU(3)/Z_3 and O(5).

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