Projective construction of non-Abelian quantum Hall liquids

Using projective construction, a generalized parton construction, we construct many non-Abelian quantum Hall (QH) states, which include the Pfaffian state at filling fraction $\nu =1/2.\mathrm{}$ The projective construction allows us to calculate bulk and edge effective theories for the constructed QH state. We illustrate how to use the bulk effective theory to calculate the ground-state degeneracy of non-Abelian QH liquids on a torus. We point out that a full description of the effective theory requires both an effective Lagrangian and the definition of electron operators. The latter generates all physical states, and defines the gauge structure of the theory.