Monopole Instability I: Negative Modes

Horváthy, P. A. and O'Raifeartaigh, L. (1986) Monopole Instability I: Negative Modes. (Preprint)

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Abstract

For monopoles with non-vanishing Higgs potential it is shown that with respect to (asymptotic) variations of the gauge potential (a) the stability problem reduces to that of a pure gauge theory on the 2-sphere (b) each topological section admits one, and only one, stable monopole, and (c) each non-stable monopole admits 2Σ(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 monopole (ii) the negative modes and (iii) the spectrum of the Hessian, on the 2-sphere, is then given. The relationship of the instability-index (2(q)-1) to the Aliyah-Singer and Witten indices is exhibited and the general theory is illustrated for the little groups U(2), U(3) and O(5).

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 06 Jul 2018 08:58
Last Modified: 24 Jul 2018 09:29
URI: http://dair.dias.ie/id/eprint/846

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