In quantum field theory, the vacuum state may be degenerate. Each pure vacuum state generates its own superselection sector. The space of all pure vacuum states often has a manifold structure called the vacuum manifold. The vacuum manifold in a homogeneous field is given by its minimum potential at all points. Vacuum manifolds arise during the process of spontaneous symmetry breaking from a group G to a subgroup H and the corresponding vacuum manifold has to be a realization of G and contain the quotient space G/H. In most cases, the new space will be G/H, although it can be larger. Not all vacuum manifolds arise due to spontaneous symmetry breaking. Supersymmetric models often contain moduli spaces which is another name for the vacuum manifold. In many cases, the vacuum manifold is parameterized by the values of permissible vacuum expectation values. This is not the case for spontaneous symmetry breaking due to fermion condensation, though. If the vacuum manifold is homotopically nontrivial, it's possible for there to be topological sectors. References Quantum field theory