Monopole-charge instability
arXiv:0909.2523 · doi:10.1142/S0217751X88000291
Abstract
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 negative modes, where the sum goes over all negative eigenvalues of the non-Abelian charge . 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).
LaTex, 38 pages. 7 figures and 2 photos. Posted for the record. Originally published 20 years ago, with Note added in 2009: Hommage to Lochlainn O'Raifeartaigh and Sidney Coleman. Some typos corrected