Infinite dimensional Grassmannian structure of two-dimensional quantum gravity
Nov, 199049 pages
Published in:
- Commun.Math.Phys. 143 (1992) 371-404
DOI:
Report number:
- UT-572-TOKYO,
- KEK-TH-272,
- KEK-PREPRINT-90-165
Citations per year
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
References(14)
Figures(0)