Geometry and W-Gravity

Abstract

The higher-spin geometries of $W_{\infty }$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_{\infty }$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\it Pathways to Fundamental Interactions}, the 16th John Hopkins Workshop on Current Problems in Particle Theory, Gothenborg, 1992.)

31 pages

Cited by in corpus (7)

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• The geometry of W3 algebra: a twofold way for the rebirth of a symmetry
• The role of complex structures in w-symmetry
• The Geometric Structure of $W_N$-Gravity
• Primary currents and Riemannian geometry in W-algebras
• Nonlinear realizations of $W_3$ symmetry
• Induced quantum gravity on a Riemann Surface