
Symmetry in Nonlinear Mathematical Physics  2009
Victor Enolski (Institute of Magnetism of NASU, Kyiv, Ukraine)
On the existence charge three SU(2) monopole: algebrogeometric approach
Abstract:
Charge three SU(2) monopole solution to the Bogomolny equation in the BPS
limit is considered within HitchinNahm
algebrogeometric construction. The Hitchin constraints are analyzed for the genus
four monopole curve with
Z_{3} symmetry. It is shown
that the moduli space of the curve covers Humbert surface H_{4}. That
leads to decomposition of the initial thetafunctions to Jacobian
theta's. Using this mashinary Hitchin conditions are explicitly resolved.
The analysis undertaken leads to the conculision that for
the given class of monopole curves only monopole with tetrahedral symmetry
exists whilst there are no monopole solutions beyond this
symmetry.

