Phase transitions in spinor quantum gravity on a lattice

Understand

We construct a well-defined lattice-regularized quantum theory formulated in terms of fundamental fermion and gauge fields, the same type of degrees of freedom as in the Standard Model.

• The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under diffeomorphisms.
• It is suitable for describing large nonperturbative and fast-varying fluctuations of metrics.
• Although the quantum curved space turns out to be on the average flat and smooth owing to the non-compressibility of the fundamental fermions, the low-energy Einstein limit is not automatic: one needs to ensure that composite metrics fluctuations propagate to long distances as compared to the lattice spacing.