GRAV In the literature: contested

Does causal dynamical triangulations have a continuum limit reproducing 4D gravity?

In plain words

One approach builds spacetime from tiny four-dimensional building blocks glued with a fixed direction of time and sums over all gluings on a computer. A genuine theory needs a point where the blocks can be made infinitely small, a continuous phase transition, and whether one exists is unsettled.

Precise statement

In 4D causal dynamical triangulations the phase diagram in bare couplings $(\kappa_{0}, \Delta)$ contains a phase C with de Sitter-like large-scale geometry; transitions bordering phase C, including the one to the bifurcation phase, show second- or higher-order signatures, while the A-C transition is first order (Ambjorn, Jordan, Jurkiewicz, Loll 2012 and later work). Determine whether a second-order critical point exists at which the lattice spacing goes to zero while large-scale geometry approaches a classical 4D solution with finite renormalized Newton constant, and compute its critical exponents. An answer is a finite-size scaling analysis at volumes large enough to fix order and exponents, with a continuum observable that converges.

What would settle it

Large-volume Monte Carlo finite-size scaling that fixes the transition order and exponents, plus a renormalized gravitational observable with a finite continuum limit.

Status in the literature

Unverified note

Higher-order transitions are reported (2012-2020) and reviewed as a possible route to a continuum limit (arXiv:2301.06068, 2023), but a renormalization study found no evidence of an ultraviolet fixed point at them (arXiv:2002.01693, 2020); not established as of 2026.