## Abstract

We consider a generalization of two-dimensional gravity to the general case of W-gravity. We present its light-cone gauge and conformal gauge formulation. In the latter case we determine the topological subsector of W-gravity in terms of βγ-theory. Using Ward identities for W_{3} gravity we derive new symmetries which are analogs of the coordinate transformation in the W_{2} case. Generalization of these symmetries to arbitrary W-algebra is proposed. We describe a geometrical realization of these symmetries using the infinite-dimensional flag bundle over the Riemann surface. W-gravity appears as the description of the geometry of this flag bundle. This is closely connected with the Segal-Wilson theory of the KP hierarchy and lattice Toda theory.

Original language | English |
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Pages (from-to) | 537-558 |

Number of pages | 22 |

Journal | Nuclear Physics B |

Volume | 360 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 19 Aug 1991 |

Externally published | Yes |