On Induced Gravity in 2-d Topological Theories
Abstract
We study 2-d φ F gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave functionals - representing the eigenstates of a vanishing flat potential - are obtained in the φ 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. For other representations a metric which is invariant under the residual gauge group is induced, apart from possible topological obstructions. Being inherited from the group metric it is rather rigid.
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