Article

# Discrete Gravity Models and Loop Quantum Gravity: a Short Review

Symmetry Integrability and Geometry Methods and Applications (Impact Factor: 1.3). 04/2012; DOI: 10.3842/SIGMA.2012.052

Source: arXiv

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**ABSTRACT:**The physical phase of causal dynamical triangulations (CDT) is known to be described by an effective, one-dimensional action in which three-volumes of the underlying foliation of the full CDT play a role of the sole degrees of freedom. Here we map this effective description onto a statistical-physics model of particles distributed on a 1d lattice, with site occupation numbers corresponding to the three-volumes. We identify the emergence of the quantum de-Sitter universe observed in CDT with the condensation transition known from similar statistical models. Our model correctly reproduces the shape of the quantum universe and allows us to analytically determine quantum corrections to the size of the universe. In the first-order approximation, these corrections lead to the widening of the CDT universe in the temporal direction. We also investigate the phase structure of the model and show that it reproduces all three phases observed in computer simulations of CDT. In addition, we predict that two other phases may exist, depending on the exact form of the discretized effective action and boundary conditions. We calculate various quantities such as the distribution of three-volumes in our model and discuss how they can be compared with CDT.Physical review D: Particles and fields 11/2012; 86(10). - [Show abstract] [Hide abstract]

**ABSTRACT:**We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows to construct a (cylindrically) consistent continuum limit of the theory.New Journal of Physics 11/2014; 16:123041. · 3.67 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The definition of a double-scaling limit represents an important goal in the development of tensor models. We take the first steps towards this goal by extracting and analysing the next-to-leading order contributions, in the 1/N expansion, for the IID tensor models. We show that the radius of convergence of the NLO series coincides with that of the leading order melonic sector. Meanwhile, the value of the susceptibility exponent at NLO is 3/2, signaling a departure from the leading order behaviour. Both pieces of information provide clues for a non-trivial double-scaling limit, for which we put forward some precise conjecture.New Journal of Physics 04/2013; · 3.67 Impact Factor

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