Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity

TL;DR

This paper establishes a general correspondence between the quantized 3BF theory and Einstein-Cartan theory, linking their observable predictions without detailed quantization, and discusses differences in spacetime volume and gravitational waves.

Contribution

It introduces a novel correspondence between quantized 3BF and Einstein-Cartan theories, enabling comparison of their predictions without full quantization.

Findings

Correspondence between 3BF and Einstein-Cartan theories established

Observable definitions derived via path integral formalism

Differences in predictions analyzed for spacetime volume and gravitational waves

Abstract

We construct a correspondence between the quantized constrained 3BF theory and the quantized Einstein-Cartan theory with contact spin-spin interaction, both of which describe the Standard Model coupled to Einstein-Cartan gravitational field. First we introduce the expectation values of observables using the path integral formalism for both theories, and then by integrating out some configuration space variables in the quantum 3BF theory we obtain the definition of the corresponding observable in the quantum Einstein-Cartan theory with contact interaction. The correspondence is a rather general result, since it can be established without actually performing the detailed quantization of either theory. Finally, we discuss the differences in the predictions of the two theories on the example of the 4-volume density of spacetime, and on the example of gravitational waves.