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Singular vectors and topological theories from Virasoro constraints via the Kontsevich-Miwa transform

1992/12/31 by Beatriz Gato-Rivera, B Gato-Rivera, A. M. Semikhatov +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Pulsars and Gravitational Waves Research #hep-th

paper · pdf · doi:10.1016/0550-3213(93)90135-c

published as Nucl.Phys.B408:133-179,1993 · 62p. LaTeX, CERN-TH.6752, IMAFF-92/8, revised (minor corrections, typos) easy-fontversion

arxiv created 1993/04/02 · openalex publication_date 1993/11/01 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. With the help of the Kontsevich-Miwa transform, we solve the Virasoro constraints on the KP hierarchy in terms of minimal models dressed with a (free) Liouville-like scalar. The dressing prescription originates in a topological (twisted N=2) theory. The Virasoro constraints are thus related to essentially the N=2 null state decoupling equations. The N=2 generators are constructed out of matter, the `Liouville' scalar, and c=-2 ghosts. By a `dual' construction involving the reparametrization c=-26 ghosts, the DDK dressing prescription is reproduced from the N=2 symmetry. As a by-product we thus observe that there are two ways to dress arbitrary d≤1 or d≥25 matter theory, that allow its embedding into a topological theory. By th e Kontsevich-Miwa transform, which introduces an infinite set of `time' variables tr, the equations ensuring the vanishing of correlators that involve BRST-exact primary states, factorize through the Virasoro generators expressed in terms of the tr. The background charge of these Virasoro generators is determined by the topological central charge.

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