arXiv subjects
Publications and source records attributed to S. Miyagi.
We investigate Yang-Mills instantons on a 7-dimensional manifold of G_2 holonomy. By proposing a spherically symmetric ansatz for the Yang-Mills connection, we have ordinary differential equations as the reduced instanton equation, and give some explicit and numerical solutions.
Anti-self-dual (ASD) Maxwell solutions on 4-dimensional hyperkähler manifolds are constructed. The N=2 supersymmetric half-flat equations are derived in the context of the Ashtekar formulation of N=2 supergravity. These equations show that the ASD Maxwell solutions have a direct connection with the solutions of the reduced N=2 supersymmetric ASD Yang-Mills equations with a special choice of gauge group. Two examples of the Maxwell solutions are presented.
The Ashtekar-Mason-Newman equations are used to construct the hyperkähler metrics on four dimensional manifolds. These equations are closely related to anti self-dual Yang-Mills equations of the infinite dimensional gauge Lie algebras of all volume preserving vector fields. Several examples of hyperkähler metrics are presented through the reductions of anti self-dual connections. For any gauge group anti self-dual connections on hyperkähler manifolds are constructed using the solutions of both Nahm and Laplace equations.