W geometry from Fedosov's deformation quantization

Abstract:

A geometric derivation of W∞ gravity based on Fedosov's deformation quantization of symplectic manifolds is presented. To lowest order in Planck's constant it agrees with Hull's geometric formulation of classical non-chiral W∞ gravity. The fundamental object is a W-valued connection one form belonging to the exterior algebra of the Weyl algebra bundle associated with the symplectic manifold. The W-valued analogs of the self-dual Yang-Mills equations, obtained from a zero curvature condition, naturally lead to the Moyal Plebanski equations, furnishing Moyal deformations of self-dual gravitational backgrounds associated with the complexified cotangent space of a two-dimensional Riemann surface. Deformation quantization of W∞ gravity is retrieved upon the inclusion of all the ℏ terms appearing in the Moyal bracket. Brief comments on non commutative geometry and M(atrix) theory are made. ©2000 Elsevier Science B.V. All rights reserved.

Año de publicación:

2000

Keywords:

• Integrable systems
• Moyal-Fedosov quantization
• strings
• Star products
• W-geometry

Fuente:

scopus