ON INDUCED GRAVITY IN 2D TOPOLOGICAL THEORIES

We study 2d phiF gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave func tionals - representing the eigenstates of a vanishing flat potential - are obtained in the phi representation. The composition of the space they describe is then analyzed: the state corresponding to the singlet representation of the gauge group describes a topological universe. F or other representations a metric which is invariant under the residua l gauge group is induced, apart from possible topological obstructions . Being inherited from the group metric, it is rather rigid.