Topological Solitons Seminar:
2 November 2011 13:00 in CM221
The Yang-Mills equations are second-order differential equations in the gauge potential, in general they are not integrable. All known solutions in four dimensions come from the Anti-Self-Duality equations, which imply the Yang-Mills equations and are fully integrable. What about higher dimensions? We explain algebraic conditions one can impose on the curvature that also imply Yang-Mills. Particularly interesting is such an example of extended Self-Duality to eight-manifolds with holonomy Spin(7). We proceed to introduce the Octonionic Instanton Equation and explore symmetry reductions and the relation of the Seiberg-Witten equations. Finally, we present explicit examples of octonionic anti-self-dual gauge fields with gauge group SU(2) on certain Spin(7)-manifolds.
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