The paper develops a formalism for reduction and inverse-reduction functors and computes the action of reduction on standard modules of V^k(sl_2), noting unbounded spectral sequences.
The MFF Singular Vectors in Topological Conformal Theories
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abstract
It is argued that singular vectors of the topological conformal (twisted $N=2$) algebra are identical with singular vectors of the $sl(2)$ Kac--Moody algebra. An arbitrary matter theory can be dressed by additional fields to make up a representation of either the $sl(2)$ current algebra or the topological conformal algebra. The relation between the two constructions is equivalent to the Kazama--Suzuki realisation of a topological conformal theory as $sl(2)\oplus u(1)/u(1)$. The Malikov--Feigin--Fuchs (MFF) formula for the $sl(2)$ singular vectors translates into a general expression for topological singular vectors. The MFF/topological singular states are observed to vanish in Witten's free-field construction of the (twisted) $N=2$ algebra, derived from the Landau--Ginzburg formalism.
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Reduction and inverse-reduction functors I: standard $\mathsf{V^k}(\mathfrak{sl}_2)$-modules
The paper develops a formalism for reduction and inverse-reduction functors and computes the action of reduction on standard modules of V^k(sl_2), noting unbounded spectral sequences.