Interacting Euclidean 3D Quantum Gravity
  We show that Euclidean 3D-gravity coupled to a Gaussian scalar massive matter field in first-order dreibein formalism gives a quantum theory which has a finite perturbative expansion around a non-vanishing background. We also discuss a possible mechanism to generate a non-trivial background metric starting from Rovelli-Smolin's loop observables. 
G.Bonacina, A.Gamba and M.Martellini