The MFF singular vectors in topological conformal theories

Semikhatov, A.M.

doi:10.1142/S0217732394001738

The MFF singular vectors in topological conformal theories

A.M. Semikhatov
(
- Lebedev Inst.
)

Dec 6, 1993

25 pages

Published in:

Mod.Phys.Lett.A 9 (1994) 1867-1896,
JETP Lett. 58 (1993) 860-869

e-Print:

hep-th/9311180 [hep-th]

DOI:

10.1142/S0217732394001738

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Abstract: (arXiv)

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.

Note:

26pp., LaTeX, REVISED

field theory: conformal
field theory: topological
dimension: 2
operator: algebra
quantum algebra: SL(2)
algebra: Kac-Moody
bosonization
phase space
gravitation
bibliography

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