$\bf W_\infty$ Gravity - a Geometric Approach

Details $\bf W_\infty$ Gravity - a Geometric Approach $\bf W_\infty$ Gravity - a Geometric Approach

1992-07-14

arxiv.org/abs/hep-th/9207048v1

Theor.Math.Phys. 93 (1992) 1268-1278; Teor.Mat.Fiz. 93 (1992) 273-285

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/BF01083525

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.

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