Three Principles for Quantum Gravity

TL;DR

This paper proposes three fundamental principles for quantum gravity—diffeomorphism symmetry, unitarity, and locality—and explores their implications, including the role of anomalies and extensions of the diffeomorphism algebra.

Contribution

It introduces a framework for understanding quantum gravity principles, emphasizing the role of anomalies and generalizations of the Virasoro algebra in multiple dimensions.

Findings

Diffeomorphism symmetry can be compatible with local observables through anomalies.

Generalization of Virasoro extension to higher dimensions is described.

Anomalies depend on the observer's spacetime trajectory, unlike in QFT.

Abstract

We postulate that the fundamental principles of Quantum Gravity are diffeomorphism symmetry, unitarity, and locality. Local observables are compatible with diffeomorphism symmetry in the presence of diff anomalies, which modify the symmetry algebra upon quantization. We describe the generalization of the Virasoro extension to the diffeomorphism algebra in several dimensions, and its off-shell representations. These anomalies can not arise in QFT, because the Virasoro-like cocycles are functionals of the observer's spacetime trajectory, which is not present in QFT. Possible implications for physics are discussed.