Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation

TL;DR

This paper introduces a conformally augmented loop quantum gravity framework that unifies various gravity theories, eliminates the Immirzi ambiguity, and explores implications of scale invariance for quantum gravity.

Contribution

It develops a new loop quantization method incorporating conformal and scale invariance applicable to multiple gravity theories, removing the Immirzi ambiguity.

Findings

Quantum geometry lacks Immirzi ambiguity.

No definitive area gaps in the new framework.

Scale invariance leads to a conserved Weyl current.

Abstract

A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general relativity and scale-invariant scalar-tensor and dilaton theories. Consequently, matter to be coupled to such theories is restricted to be conformal or scale invariant. Standard model-type systems naturally fall into this category. The new loop quantization follows from a novel conformally generalized Holst action principle. In contrast to standard loop quantum gravity, the resulting quantum geometry is not beset by the Immirzi ambiguity and has no definitive area gaps within the considered large class of theories of gravitation. As an additional feature, the scale invariance gives rise to a conserved Weyl current and we discuss briefly its possible implication on the problem of time in quantum gravity.