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

Dec, 1992
59 pages
Published in:
  • Nucl.Phys.B 408 (1993) 133-179
e-Print:
Report number:
  • CERN-TH-6752-92,
  • IMAFF-92-8

Citations per year

199319992005201120170123456
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 N=2N=2) theory with topological central charge \ctop\neq 3. The corresponding N=2N=2 generators are constructed out of matter, a (free) Liouville-like scalar, and c=2c=-2 ghosts. By a different construction involving the reparametrization c=26c=-26 ghosts, the DDK dressing prescription is reproduced from N=2N=2 symmetry. As a by-product we thus observe that there are two ways to dress arbitrary d1d25d \leq 1\bigcup d \geq 25 matter theory, which allow its embedding into a topological theory. By the Kontsevich-Miwa transform, which introduces an infinite set of `time' variables trt_r, the equations ensuring the vanishing of correlators that involve BRST-exact primary states, factorize through Virasoro generators expressed in terms of the trt_r. 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