Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations

Abstract

An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate technical tools, one is interested in measuring and classifying how the quantum fluctuations of geometry alter the behaviour of matter, compared with that on a fixed background geometry. In the simplified context of two dimensions, we show how a method invented to analyze the critical behaviour of spin systems on flat lattices can be adapted to the fluctuating ensemble of curved spacetimes underlying the Causal Dynamical Triangulations (CDT) approach to quantum gravity. We develop a systematic counting of embedded graphs to evaluate the thermodynamic functions of the gravity-matter models in a high- and low-temperature expansion. For the case of the Ising model, we compute the series expansions for the magnetic susceptibility on CDT lattices and their duals up to orders 6 and 12, and analyze them by ratio method, Dlog Padé and differential approximants. Apart from providing evidence for a simplification of the model's analytic structure due to the dynamical nature of the geometry, the technique introduced can shed further light on criteria à la Harris and Luck for the influence of random geometry on the critical properties of matter systems.

40 pages, 15 figures, 13 tables

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Cited by in corpus (15)

• Nonperturbative Quantum Gravity
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
• A new continuum limit of matrix models
• Shaken, but not stirred - Potts model coupled to quantum gravity
• Imposing causality on a matrix model
• Summing over all Topologies in CDT String Field Theory
• An Analytical Analysis of CDT Coupled to Dimer-like Matter
• Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Sums over geometries and improvements on the mean field approximation
• Generic Ising Trees
• Potts model coupled to causal triangulations
• Quantum Gravity from Simplices: Analytical Investigations of Causal Dynamical Triangulations
• Critical region for an Ising model coupled to causal dynamical triangulations
• Phase transition for the Ising model on the Critical Lorentzian triangulation