Quantum Gravity and Matter Counting Graphs on Causal Dynamical Triangulations.pdf

SPIN-06/32 ITP-UU-06/38 Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations 6 0 1 0 D. Benedetti and R. Loll 2 v o Spinoza Institute and Institute for Theoretical Physics, N Utrecht University, 4 Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands. 1 1 v 5 7 0 Abstract 1 1 An outstanding challenge for models of non-perturbative quantum gravity is the consistent 6 formulation and quantitative evaluation of physical phenomena in a regime where geome- 0 / try and matter are strongly coupled. After developing appropriate technical tools, one is c q interested in measuring and classifying how the quantum fluctuations of geometry alter the r- behaviour of matter, compared with that on a fixed background geometry. g In the simplified context of two dimensions, we show how a method invented to analyze : v the critical behaviour of spin systems on flat lattices can be adapted to the fluctuating ensem- i X ble of curved spacetimes underlying the Causal Dynamical Triangulations (CDT) approach r to quantum gravity. We develop a systematic counting of embedded graphs to evaluate the a thermodynamic functions of the gravity-matter models in a high- and low-temperature ex- pansion. 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 Pad´e and differential approximants. Apart from pr