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Register a new userThe Semiclassical Limit of Causal Dynamical Triangulations
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Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations (CDT) is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature of this semiclassical limit we present a detailed study of the three-volume data, which allows us to re-confirm the de Sitter structure, exhibit short-distance discretization effects, and make a first detailed investigation of the presence of higher-order curvature terms in the effective action for the scale factor. Technically, we make use of a novel way of fixing the total four-volume in the simulations.
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We consider the model of hard dimers coupled to two-dimensional Causal Dynamical Triangulations (CDT) with all dimer types present and solve it exactly subject to a single restriction. Depending on the dimer weights there are, in addition to the usual gravity phase of CDT, two tri-critical and two dense dimer phases. We establish the properties of these phases, computing their cylinder and disk amplitudes, and their scaling limits.
Causal dynamical triangulations (CDT) constitute a background independent, nonperturbative approach to quantum gravity, in which the gravitational path integral is approximated by the weighted sum over causally well-behaving simplicial manifolds i.e. causal triangulations. This thesis is an analysis of the data from the Monte Carlo computer simulations of CDT in 3+1 dimensions. It is confirmed here that there exist the semiclassical limit of CDT for so-called (4,1) (or equivalent (1,4)) simplices, being a discrete version of the mini-superspace model. Next, the form of the corresponding discrete action is investigated. Furthermore, it is demonstrated that the effective, semiclassical solution works also after the inclusion of remaining (3,2) and (2,3) simplices, treated collectively. A specific form of the resulting extended discrete action is examined and a transition from the broader framework to the former narrower one is shown.
In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came from numerical results on four-dimensional causal dynamical triangulations (CDT) [Ambjorn et al., Phys. Rev. Lett. 95 (2005) 171]. Since then little progress has been made in analytically understanding the numerical results coming from the CDT approach and showing that they remain valid when taking the continuum limit. Here we argue that the spectral dimension can be determined from a model with fewer degrees of freedom obtained from the CDTs by radial reduction. In the resulting toy model we can take the continuum limit analytically and obtain a scale dependent spectral dimension varying from four to two with scale and having functional behaviour exactly of the form which was conjectured on the basis of the numerical results.
We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for islands in determining the entanglement wedge.
We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also proof that there is only one analytic nonlinear electrodynamics presenting no birefringence.
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