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On the existence of non-abelian monopoles: the algebro-geometric approach | | H.W. Braden
; V.Z. Enolski
; | | Date: |
20 Sep 2010 | | Abstract: | We develop the Atiyah-Drinfeld-Manin-Hitchin-Nahm construction to study SU(2)
non-abelian charge 3 monopoles within the algebro-geometric method. The method
starts with finding an algebraic curve, the monopole spectral curve, subject to
Hitchin’s constraints. We take as the monopole curve the genus four curve that
admits a $C_3$ symmetry,
$eta^3+alphaetazeta^2+etazeta^6+gammazeta^3-eta=0$, with real
parameters $alpha$, $eta$ and $gamma$. In the case $alpha=0$ we prove that
the only suitable values of $gamma/eta$ are $pm 5sqrt{2}$ ($eta$ is
given below) which corresponds to the tetrahedrally symmetric solution. We then
extend this result by continuity to non-zero values of the parameter $alpha$
and find finally a {em new} one-parameter family of monopole curves with $C_3$
symmetry. | | Source: | arXiv, 1009.3837 | | Services: | Forum | Review | PDF | Favorites | |
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