Unitary representations of the Virasoro and super-Virasoro algebras

Abstract

Abstract.It is shown that a method previously given for constructing representations of the Virasoro algebra out of representations of affine KacMoody algebras yields the full discrete series of highest weight irreducible representations of the Virasoro algebra. The corresponding method for the super-Virasoro algebras (i.e. the Neveu-Schwarz and Ramond algebras) is described in detail and shown to yield the full discrete series of irreducible highest weight representations.

Parafermion Hall states from coset projections of abelian conformal theories

“…Therefore, this approach is not practical for a detailed description of the parafermion conformal theory. In Sections 3 and 4, we consider the better known description [19] of Z k parafermions in terms of the coset construction [20]:…”

Unitary minimal models of Script SScript W(3/2,3/2,2) superconformal algebra and manifolds ofG2holonomy

“…The method we use was first proposed in [20] for coset (B.4). The su(2) affine algebra is generated by 3 currents J i , i = 1, 2, 3:…”

Doped Heisenberg chains: Spin-S generalizations of the supersymmetric t-J model

“…[28,29]). Different from these models, however, one finds two branches of low lying modes in the magnetic sector which at small (large) doping can be identified with higher level SU (2) invariant effective low energy field theory for the S > 1 models introduced here is possible by using the fact that the minimal models can be obtained within a GKO coset construction applied to [30,31] …”