  We consider stable and semistable principal bundles over a smooth projective
real algebraic curve, equipped with a real or pseudo-real structure in the
sense of Atiyah. After fixing suitable topological invariants, one can build a
suitable gauge theory, and show that the resulting moduli spaces of pseudo-real
bundles are connected. This in turn allows one to describe the various fixed
point varieties on the complex moduli spaces under the action of the real
involutions on the curve and the structure group.
