7 Higgs branches and hyperkähler manifolds

So far we only considered the branch of the moduli space of the supersymmetric vacua where the scalar $\Phi$ in the vector multiplet is nonzero, and all the hypermultiplets are zero. Instead let us consider a branch where $\Phi =0$, but the hypermultiplet scalars are nonzero. This branch is called the Higgs branch.