Four dimensional Riemannian general relativity as a spontaneous symmetry breaking

TL;DR

This paper proposes a novel approach where four-dimensional Riemannian general relativity emerges from a phase transition driven by spontaneous symmetry breaking within a quantum field theory framework, utilizing operator algebraic methods.

Contribution

It introduces a new perspective on deriving 4D Euclidean gravity from quantum field theory through symmetry breaking in a hyperfinite von Neumann algebra.

Findings

Recovery of 4D Riemannian gravity from quantum phase transition

Identification of a formal temperature for the phase transition

Application of operator algebraic approach to quantum gravity

Abstract

In this paper $4$ dimensional Riemannian (or Euclidean) vacuum general relativity is recovered from a phase transition by spontaneous symmetry breaking within a quantum field theory (all in the sense of the operator algebraic approach to quantum field theory) provided by the unique ${\rm II}_1$ hyperfinite factor von Neumann algebra. The formal temperature of this phase transition is $T=\frac{1}{2}T_{\rm Planck}\approx7.06\times 10^{31}{\rm K}$. (For an extended abstract see the text.)