3-DIMENSIONAL FIELD-THEORIES FROM INFINITE-DIMENSIONAL LIE-ALGEBRAS

A procedure for constructing topological actions from centrally extended Lie algebras is introduced. For a Kac-Moody algebra, this produces the three-dimensional Chern-Simons theory, while for the Virasoro algebra, the result is a new three-dimensional topological field theory whose physical states satisfy the Virasoro Ward identity. This topological field theory is shown to be a first order formulation of two-dimensional induced gravity in the chiral gauge. The extension to W3 gravity is discussed.