Integrability and Scheme-Independence of Even Dimensional Quantum Geometry Effective Action

Abstract

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.

Latex, 26 pages. errors in some sentences and typo corrected

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• Constructing the independent basis of total derivative curvature-dependent terms in $6D$
• Fractal Structure of 4D Euclidean Simplicial Manifold
• Casimir energy on the sphere and 6D CFT trace anomaly