Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition

TL;DR

This paper proposes a quantum gravity model based on local Lorentz symmetry and coordinate invariance, where the inverse vierbein is absent at tree level, and fermionic fluctuations induce gravity.

Contribution

It introduces the irreversible vierbein postulate, a novel approach where the inverse vierbein is excluded at tree level, leading to gravity emerging from fermionic fluctuations.

Findings

Fermionic fluctuations induce a non-zero gravitational background.

The model maintains local Lorentz and coordinate invariance.

The inverse vierbein is absent at tree level, supporting emergent gravity.

Abstract

We formulate a model for quantum gravity based on the local Lorentz symmetry and general coordinate invariance. A key idea is the irreversible vierbein postulate that a tree-level action for the model at a certain energy scale does not contain an inverse vierbein. Under this postulate, only the spinor becomes a dynamical field, and no gravitational background field is introduced in the tree-level action. In this paper, after explaining the transformation rules of the local Lorentz and general-coordinate transformations in detail, a tree-level action is defined. We show that fermionic fluctuations can induce a nonvanishing gravitational background field.