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.)
Categories: math-ph gr-qc hep-th math.MP