Phase transitions in spinor quantum gravity on a lattice

TL;DR

This paper develops a lattice quantum gravity model with fermions and gauge fields, identifying phase transitions that could lead to Einstein gravity and potentially explain a zero cosmological constant.

Contribution

It introduces a lattice-regularized quantum gravity theory with fermions and gauge fields, analyzing its phase structure and the emergence of Einstein gravity at a phase transition.

Findings

Multiple phases separated by second order phase transitions.

Existence of a phase with spontaneous chiral symmetry breaking.

Potential automatic zero cosmological constant at the phase transition.

Abstract

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. One way to guarantee this is to stay at a phase transition. We develop a lattice mean field method and find that the theory typically has several phases in the space of the dimensionless coupling constants, separated by the second order phase transition surface. For example, there is a phase with a spontaneous breaking of chiral symmetry. The effective low-energy Lagrangian for the ensuing Goldstone field is explicitly diffeomorphism-invariant. We expect that the Einstein gravitation is achieved at the phase transition. A bonus is that the cosmological constant is probably automatically zero.