Infinite dimensional Grassmannian structure of two-dimensional quantum gravity

Nov, 1990
49 pages
Published in:
  • Commun.Math.Phys. 143 (1992) 371-404
Report number:
  • UT-572-TOKYO,
  • KEK-TH-272,
  • KEK-PREPRINT-90-165

Citations per year

198719972007201720250102030
Abstract: (Springer)
We study the infinite dimensional Grassmannian structure of 2D quantum gravity coupled to minimal conformal matters, and show that there exists a large symmetry, theW1+∞ symmetry. Using this symmetry structure, we prove that the square root of the partition function, which is a τ function of thep-reduced KP hierarchy, satisfies the vacuum condition of theW1+∞ algebra. We further show that this condition is reduced to the vacuum condition of theWp algebra when the redundant variables for thep-reduction are eliminated. This mechanism also gives a prescription for extracting theWp algebra from theW1+∞ algebra.
  • quantum gravity
  • dimension: 2
  • field theory: conformal
  • partition function
  • algebra: W(infinity)
  • algebra: Grassmann
  • matrix model
  • string model
  • field equations
  • Kadomtsev-Petviashvili equation