Let G be a complex reductive Lie group, and consider Higgs(G) the moduli space of G-Higgs bundles. The choice of a maximal torus T<G defines a BBB brane Higgs(T)⊂Higgs(G) (the Cartan brane). According to Kapustin--Witten,  this corresponds under mirror symmetry to a BAA brane in Higgs(LG), where LG denotes the Langlands dual group. In this talk I will explain what this BAA should be for rank two Higgs bundles. This is joint work with Emilio Franco.