Constructing SU(N) fractional instantons

Understand

We study self-dual SU(N) gauge field configurations on the 4 torus with twisted boundary conditions, known as fractional instantons.

• Focusing on the minimum non-zero action case, we generalize the constant field strength solutions discovered by `t Hooft and valid for certain geometries.
• For the general case, we construct the vector potential and field strength in a power series expansion in a deformation parameter of the metric.
• The next to leading term is explicitly computed.