Lax Pair Formulation of the W-gravity Theories in two Dimensions

Details Lax Pair Formulation of the W-gravity Theories in two Dimensions Lax Pair Formulation of the W-gravity Theories in two Dimensions

1992-01-28

arxiv.org/abs/hep-th/9201060v1

Int.J.Mod.Phys. A7 (1992) 6907-6932

Physics

High Energy Physics

High Energy Physics - Theory

26 pages

Scientific paper

The Lax pair formulation of the two dimensional induced gravity in the light-cone gauge is extended to the more general $w_N$ theories. After presenting the $w_2$ and $w_3$ gravities, we give a general prescription for an arbitrary $w_N$ case. This is further illustrated with the $w_4$ gravity to point out some peculiarities. The constraints and the possible presence of the cosmological constants are systematically exhibited in the zero-curvature condition, which also yields the relevant Ward identities. The restrictions on the gauge parameters in presence of the constraints are also pointed out and are contrasted with those of the ordinary 2d-gravity.

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