Matter Dependence of the String Susceptibility Exponent in Four-Dimensional Simplicial Quantum Gravity

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.

Section: Jhep10(2013)100mentioning

confidence: 99%

Euclidian 4d quantum gravity with a non-trivial measure term

Ambjørn

Glaser²,

Görlich

et al. 2013

“…Asymptotically safe gravity in viewpoint of the fractal space-time structure has been studied in [110][111][112][113]. Analyses with lattice simulation have been performed in [114][115][116][117][118][119][120][121][122][123][124]. 6 See related studies [138][139][140][141].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system

Hamada

Yamada

2017

Abstract:We study asymptotic safety of models of the higher derivative quantum gravity with and without matter. The beta functions are derived by utilizing the functional renormalization group, and non-trivial fixed points are found. It turns out that all couplings in gravity sector, namely the cosmological constant, the Newton constant, and the R 2 and R 2 µν coupling constants, are relevant in case of higher derivative pure gravity. For the Higgs-Yukawa model non-minimal coupled with higher derivative gravity, we find a stable fixed point at which the scalar-quartic and the Yukawa coupling constants become relevant. The relevant Yukawa coupling is crucial to realize the finite value of the Yukawa coupling constants in the standard model.

“…Arguments were put forward that a sufficient amount of matter might ameliorate the results [23,24] (see also [25]). With gauge fields the SDT model acquires a third phase, called crinkled [26,27] or smooth [28,29]. This phase was also found without gauge fields upon adding a so-called 'measure term' [30] to the action, with a new parameter that represents the number of gauge fields [26,27,31].…”

Section: Introductionmentioning

confidence: 98%

“…This phase was also found without gauge fields upon adding a so-called 'measure term' [30] to the action, with a new parameter that represents the number of gauge fields [26,27,31]. Study of this new phase led to a confusing state of affairs: whereas some authors did not convincingly find physically attractive behavior [27,31], others found evidence for a higher-than-first order transition [28] with a susceptibility exponent suggestive of emerging graviton degrees of freedom [29,25]. Recent studies of the third phase found that its spectral dimension also depends on the distance scale [32,33].…”

Section: Introductionmentioning

confidence: 99%

Continuum interpretation of the dynamical-triangulation formulation of quantum Einstein gravity

Smit

2013

In the time-space symmetric version of dynamical triangulation, a nonperturbative formulation of quantum Einstein gravity, numerical simulations without matter have shown two phases, with spacetimes that are either crumpled or elongated like branched-polymers, with strong evidence of a first-order transition between them. These properties have generally been considered unphysical. Using previously unpublished numerical results, we give an interpretation in terms of continuum spacetimes that have constant positive and negative curvature, respectively in the 'elongated' and 'crumpled' phase. The magnitude of the positive curvature leads naturally to average spacetimes consisting solely of baby-universes in a branched-polymer structure, whereas the negative curvature accommodates easily a large mother universe, albeit with a crumpling singularity. Nevertheless, there is evidence for scaling in the crumpled phase, which we compare with the well-known scaling in the elongated phase. Using constraint effective-action models we analyze existing numerical susceptibility-data of the phase transition and determine the behavior of the average Regge-curvature. We propose a renormalization of the Regge curvature and compare it to the curvature of the above continuum spacetimes, and also to the curvature implied by the Gauss-Bonnet theorem in the continuum. The latter involves a more benign multiplicative renormalization and suggests that simulations at larger volumes are needed to settle to order of the phase transition.