Four dimensional Riemannian general relativity as a spontaneous symmetry breaking

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 ${\mathrm{I}\mathrm{I}}_1$ hyperfinite factor von Neumann algebra. The formal temperature of this phase transition is $T=\frac{1}{2}{T}_{\mathrm{P}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{k}}\approx 7.06\times {10}^{31}\mathrm{K}$. (For an extended abstract see the text.)