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    The MFF Singular Vectors in Topological Conformal Theories

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    It is argued that singular vectors of the topological conformal (twisted N=2N=2) algebra are identical with singular vectors of the sl(2)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)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)⊕u(1)/u(1)sl(2)\oplus u(1)/u(1). The Malikov--Feigin--Fuchs (MFF) formula for the sl(2)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=2N=2 algebra, derived from the Landau--Ginzburg formalism.Comment: 26pp., LaTeX, REVISE
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