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

TL;DR

This paper explores how integrability conditions shape the effective action in even-dimensional quantum geometry, ensuring scheme independence and diffeomorphism invariance, with extensions to six dimensions and a proposed model.

Contribution

It demonstrates the scheme-independent, diffeomorphism-invariant form of the 4D quantum geometry effective action and extends the framework to propose a model for 6D quantum geometry.

Findings

Effective action in 4D quantum geometry is scheme-independent and diffeomorphism invariant.

Generalization of integrability conditions to 6D quantum geometry.

Proposal of a model for 6D 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.