J. Jurkiewicz

Second-order phase transition in causal dynamical triangulations.

Causal dynamical triangulations are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially be used to define a continuum limit in the conventional sense of nongravitational lattice theories.Causal Dynamical Triangulations (CDT) are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially be used to define a continuum limit in the conventional sense of nongravitational lattice theories.

Second- and first-order phase transitions in causal dynamical triangulations

Causal Dynamical Triangulations (CDT) is a proposal for a theory of quantum gravity, which implements a path-integral quantization of gravity as the continuum limit of a sum over piecewise flat spacetime geometries. We use Monte Carlo simulations to analyse the phase transition lines bordering the physically interesting de Sitter phase of the four-dimensional CDT model. Using a range of numerical criteria, we present strong evidence that the so-called A-C transition is first order, while the B-C transition is second order. The presence of a secondorder transition may be related to an ultraviolet fixed point of quantum gravity and thus provide the key to probing physics at and possibly beyond the Planck scale.

Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields

We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to d massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a c=1 “barrier”, analogous to the c=1 barrier encountered in non-critical string theory, only the CDT transition is easier to be detected numerically. For d⩽1 we observe time-translation invariance and geometries entirely governed by quantum fluctuations around the uniform toroidal topology put in by hand. For d>1 the effective average geometry is no longer toroidal but “semiclassical” and spherical with Hausdorff dimension dH=3. In the d>1 sector we study the time dependence of the semiclassical spatial volume distribution and show that the observed behavior is described by an effective mini-superspace action analogous to the actions found in the de Sitter phase of three- and four-dimensional pure CDT simulations and in the three-dimensional CDT-like Hořava–Lifshitz models.

Four-dimensional dynamically triangulated gravity coupled to matter.

We investigate the phase structure of four-dimensional quantum gravity coupled to Ising spins or Gaussian scalar fields by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial manifolds, and the matter fields are located in the center of the 4-simplices, which constitute the building blocks of the manifolds. We find that the coupling between spin and geometry is weak away from the critical point of the Ising model. At the critical point there is clear coupling, which qualitatively agrees with that of gaussian fields coupled to gravity. In the case of pure gravity a transition between a phase with highly connected geometry and a phase with very dilute geometry has been observed earlier. The nature of this transition seems unaltered when matter fields are included. It was the hope that continuum physics could be extracted at the transition between the two types of geometries. The coupling to matter fields, at least in the form discussed in this paper, seems not to improve the scaling of the curvature at the transition point.