Integrability and Scheme-Independence of Even Dimensional Quantum   Geometry Effective Action
  We investigate how the integrability conditions for conformal anomalies constrain the form of the effective action in even-dimensional quantum geometry. We show that the effective action of four-dimensional quantum geometry (4DQG) satisfying integrability has a manifestly diffeomorphism invariant and regularization scheme-independent form. We then generalize the arguments to six dimensions and propose a model of 6DQG. A hypothesized form of the 6DQG effective action is given. 
Ken-ji Hamada (KEK)