Higgs Bundles and (A, B, A)-Branes

Through the action of anti-holomorphic involutions on a compact Riemann surface I pound we construct families of (A, B, A)-branes in the moduli spaces of G (c) -Higgs bundles on I pound. We study the geometry of these (A, B, A)-branes in terms of spectral data and show they have the structure of real integrable systems.