Vacuum manifold

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 and is called the vacuum manifold.

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 many cases, it would simply be G/H, although it could be larger.