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arXiv 0909.2523hep-th
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单极电荷不稳定性

Monopole-charge instability

P. A. Horvathy, L. O'Raifeartaigh, J. H. Rawnsley

摘要:

对于具有非零Higgs势的单极子,本文证明了:对于“Brandt-Neri-Coleman型”变分,(a)稳定性问题归结为双球上纯规范理论的稳定性问题;(b)每个拓扑扇区允许且仅允许一个稳定的负荷;(c)每个不稳定的负荷允许$2\sum_{q<0} (2|q|-1)$负模.其中该和覆盖非阿贝尔电荷$Q$的所有负本征值$q$。给出了2-球面上唯一稳定荷、负模和Hessian谱的显式构造。解释了剩余群中的环的关系。负模式与适当的能量减少双球相切。给出了小群U(2),U(3),SU(3)/Z_3和O(5)的一般理论。

英文摘要:

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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