Singular Vectors and Topological Theories from Virasoro Constraints via the Kontsevich-Miwa Transform

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 $d\le 1$ or $d\ge 25$ matter theory, that allow its embedding into a topological theory. By th e Kontsevich-Miwa transform, which introduces an infinite set of `time' variables $t_r$, the equations ensuring the vanishing of correlators that involve BRST-exact primary states, factorize through the Virasoro generators expressed in terms of the $t_r$. The background charge of these Virasoro generators is determined by the topological central charge.

62p. LaTeX, CERN-TH.6752, IMAFF-92/8, revised (minor corrections, typos) easy-fontversion

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• Transmutations between Singular and Subsingular Vectors of the N=2 Superconformal Algebras
• The Non-Critical N=2 String is an sl(2|1) Theory
• Families of Singular and Subsingular Vectors of the Topological N=2 Superconformal Algebra
• Spectral Flows and Twisted Topological Theories
• Topological Descendants: DDK and KM Realizations
• The Even and the Odd Spectral Flows on the N=2 Superconformal Algebras
• Nonlinear Schrodinger Equations and N=2 Superconformal Algebra
• TOPOLOGICAL MATTER, MIRROR SYMMETRY AND NON-CRITICAL (SUPER)STRINGS
• Topological supergravity structure of non-critical superstring theories