${\mathbf{W}}_{\infty }$ Gravity - a Geometric Approach

Abstract

A brief review is given of an adaptation of the coadjoint orbit method appropriate for study of models with infinite-dimensional symmetry groups. It is illustrated on several examples, including derivation of the WZNW action of induced $D=2$ $(N,0)$ supergravity. As a main application, we present the geometric action on a generic coadjoint orbit of the deformed group of area preserving diffeomorphisms. This action is precisely the anomalous effective WZNW action of $D=2$ matter fields coupled to chiral $W_{\infty }$ gravity background. Similar actions are given which produce the {\em KP} hierarchy as on-shell equations of motion.

13 pages, BGU-92/11/July-PH, LaTeX

References in corpus (2)

• Interaction of Discrete States in Two-Dimensional String Theory
• String field actions from W-infinity

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