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Some new constructions of vertex algebras and their modules in LCFT

We shall first review some basic constructions in the representation theory of $C_2$ cofinite VOAs in LCFT. They carry the structure of certain extensions of non-rational Virasoro vertex algebras. Next we shall discuss our recent realizations of affine vertex algebras $V_k(sl(2))$, and show how one can obtain realization of their logarithmic modules. We will also present a properties of new logarithmic VOAs, called the R^(p) algebras, present their different realizations and prove certain interesting conjectures related to them (this part is based on recent joint work with T. Creutzig, N. Genra and J. Yang). Some applications in the representation theory of affine vertex algebras will be also discussed.

vertex algebras, affine vertex algebras ; logarithmic conformal field theory

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