Gauge Theory of Quantum Gravity

TL;DR

This paper develops a gauge theory framework for quantum gravity using an internal metric and $SL(2,C)$ symmetry, which reduces to Einstein's gravity at low energies and is quantized on a Planck-scale lattice.

Contribution

It introduces a novel gauge theory formulation of quantum gravity with an internal metric and demonstrates its quantization on a lattice, ensuring unitarity and finiteness.

Findings

Emergence of Einstein's gravity at low energies

Bounded Hamiltonian in a fixed gauge

Finite, unitary quantum gravity on a Planck-scale lattice

Abstract

A gauge theory of quantum gravity is formulated, in which an internal, field dependent metric is introduced which non-linearly realizes the gauge fields on the non-compact group $SL(2,C)$, while linearly realizing them on $SU(2)$. Einstein's $SL(2,C)$ invariant theory of gravity emerges at low energies, since the extra degrees of freedom associated with the quadratic curvature and the internal metric only dominate at high energies. In a fixed internal metric gauge, only the the $SU(2)$ gauge symmetry is satisfied, the particle spectrum is identified and the Hamiltonian is shown to be bounded from below. Although Lorentz invariance is broken in this gauge, it is satisfied in general. The theory is quantized in this fixed, broken symmetry gauge as an $SU(2)$ gauge theory on a lattice with a lattice spacing equal to the Planck length. This produces a unitary and finite theory of quantum gravity.