Abstract
Abstract We explore an extended coupling constant space of 4d regularized Euclidean quantum gravity, defined via the formalism of dynamical triangulations. We add a measure term which can also serve as a generalized higher curvature term and determine the phase diagram and the geometries dominating in the various regions. A first order phase transition line is observed, but no second order transition point is located. As a consequence we cannot attribute any continuum physics interpretation to the so-called crinkled phase of 4d dynamical triangulations.
Highlights
JHEP10(2013)100 add higher order curvature terms to the Einstein action in such a way that the theory becomes renormalizable
We explore an extended coupling constant space of 4d regularized Euclidean quantum gravity, defined via the formalism of dynamical triangulations
As described in the Introduction, introducing β as an additional coupling constant in DTregularized Euclidean Quantum gravity is potentially very interesting. It could unite a number of different approaches to quantum gravity: the DT lattice approach, the higher curvature approach leading to asymptotic freedom and the asymptotic safety approach based on the existence of a non-Gaussian UV fixed point
Summary
Viewing the modification of the measure term as part of the action, our action depends on three bare coupling constants κ2, κ4 and β. We use Monte Carlo simulations to study expectation values of observables in the ensemble defined by the partition function (2.1). We will use Monte Carlo simulations to generate a number of independent configurations for each value of κ2 and β in a grid in the (κ2, β)-plane with β between 0 and −2 varied in steps of δβ = 0.2 and κ2 between 0.5 and 1.5 varied in steps of δκ2 = 0.1 Where Nconf denotes the number of Monte Carlo generated independent configurations at a particular value of coupling constants and Oi denotes the value of the observable O calculated for the ith configuration, i = 1, .
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