Singular vectors and topological theories from Virasoro constraints via the Kontsevich-Miwa transform
Dec, 199259 pages
Published in:
- Nucl.Phys.B 408 (1993) 133-179
e-Print:
- hep-th/9212113 [hep-th]
Report number:
- CERN-TH-6752-92,
- IMAFF-92-8
Citations per year
Abstract:
We use the Kontsevich-Miwa transform to relate the different pictures describing matter coupled to topological gravity in two dimensions: topological theories, Virasoro constraints on integrable hierarchies, and a DDK-type formalism. Via the Kontsevich-Miwa transform, the Virasoro constraints on the KP hierarchy imply null vector decoupling equations in minimal models dressed with an extra scalar. The corresponding dressed null vectors are essentially BRST-exact primary states in a topological (twisted ) theory with topological central charge \ctop\neq 3. The corresponding generators are constructed out of matter, a (free) Liouville-like scalar, and ghosts. By a different construction involving the reparametrization ghosts, the DDK dressing prescription is reproduced from symmetry. As a by-product we thus observe that there are two ways to dress arbitrary matter theory, which allow its embedding into a topological theory. By the Kontsevich-Miwa transform, which introduces an infinite set of `time' variables , the equations ensuring the vanishing of correlators that involve BRST-exact primary states, factorize through Virasoro generators expressed in terms of the . The background charge of these Virasoro generators is determined in terms of the topological central charge.- gravitation: topological
- coupling: matter
- matter: coupling
- dimension: 2
- field theory: conformal
- constraint: Virasoro
- decoupling
- decoupling: coupling
- Kadomtsev-Petviashvili equation: hierarchy
- invariance: Becchi-Rouet-Stora
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