Yang--Mills sphalerons in all even spacetime dimensions $d=2k$, $k>2$ : $k$=3,4

Abstract

The classical solutions to higher dimensional Yang--Mills (YM) systems, which are integral parts of higher dimensional Einstein--YM (EYM) systems, are studied. These are the gravity decoupling limits of the fully gravitating EYM solutions. In odd spacetime dimensions, depending on the choice of gauge group, these are either topologically stable or unstable. Both cases are analysed, the latter numerically only. In even spacetime dimensions they are always unstable, describing saddle points of the energy, and can be described as {\it sphalerons}. This instability is analysed by constructing the noncontractible loops and calculating the Chern--Simons (CS) charges, and also perturbatively by numerically constructing the negative modes. This study is restricted to the simplest YM system in spacetime dimensions $d=6,7,8$, which is amply illustrative of the generic case.

arXiv comment16 pages, 3 figures ; comments added, to appear in J. Phys. A

References in corpus (7)

• Black Holes in Magnetic Monopoles
• Gravitating Monopole Solutions II
• The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections
• Higher order curvature generalisations of Bartnick-McKinnon and coloured black hole solutions in $d=5$
• Particle-like solutions to higher order curvature Einstein--Yang-Mills systems in d dimensions
• On the supersymmetric non-abelian Born-Infeld action
• Einstein-Yang-Mills Sphalerons and Level Crossing

Cited by in corpus (2)

• No hair conjecture, nonabelian hierarchies and anti-de Sitter spacetime
• Features of gravity-Yang-Mills hierarchies in d-dimensions