Real slices of the moduli space of Higgs bundles

Through the hyperkähler structure of the moduli space of Higgs bundles for complex groups we shall construct three natural involutions whose fixed points in the moduli space give branes in the A-model and B-model with respect to each of the complex structures. Then, by means of spectral data and K-theory, we shall look at these branes and their topological invariants, and propose what the dual branes should be under Langlands duality.