The rational and C2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c̃ < 0 and C if c̃ = 0. If c̃ > 0, it is an extension of discrete Virasoro vertex operator algebra L(cp,q, 0) by its irreducible modules. It is also proved that for any rational and C2-cofinite sim...

We study the nonunitary representations of N = 2 Super Virasoro algebra for the rational central charges ĉ < 1. The resolutions for the irreducible representations of N = 2 SV ir in terms of the ”2-d gravity modules” are obtained and their characters are computed. The correspondence between N = 2 nonunitary ”minimal” models and the Virasoro minimal models + 2-d gravity is shown at the level of ...

We give expressions for the singular vectors in the highest weight representations of the Virasoro algebra. We verify that the expressions — which take the form of a product of operators applied to the highest weight vector — do indeed define singular vectors. These results explain the patterns of embeddings amongst Virasoro algebra highest weight representations. Conformal field theory relies ...

An N2 dimensional representation of the periodic Temperley-Lieb algebra TLL(x) is presented. It is also a representation of the cyclic group ZN . We choose x = 1 and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamilto...

We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-dimensional Lie algebra (constructed in [16]) is a generalization of the classical Virasoro algebra to the case of two space variables. Two main examples of integrable equations we obtain are quite well known. We show t...

We comment on the conformal boundary states of the c = 1 free boson theory on a circle which do not preserve the U(1) symmetry. We construct these Virasoro boundary states at a generic radius by a simple asymmetric shift orbifold acting on the fundamental boundary states at the self-dual radius. We further calculate the boundary entropy and find that the Virasoro boundary states at irrational r...

The notion of vertex operator algebra ([B], [FHL], [FLM]) is the algebraic counterpart of the notion of what is now usually called “chiral algebra” in conformal field theory, and vertex operator algebra theory generalizes the theories of affine Lie algebras, the Virasoro algebra and representations (cf. [B], [DL], [FLM], [FZ]). It has been well known (cf. [FZ], [L1]) that the irreducible highes...