Scaling structures in four-dimensional simplicial gravity

Egawa, Hiroshi S.; Hotta, T.; Izubuchi, Taku; Tsuda, N.; Yukawa, Tetsuyuki

doi:10.1016/s0920-5632(96)00774-8

Cited by 6 publications

(7 citation statements)

References 6 publications

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“…where Γ[n] is the Gamma function. Thanks to above relations (126) and (128), the trace for the eigenvalues of the derivative operator can be evaluated in curved space.…”

Section: Heat Kernel Tracementioning

confidence: 99%

Non-minimal coupling in Higgs–Yukawa model with asymptotically safe gravity

Oda

Yamada

2016

Class. Quantum Grav.

124

127

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We study the fixed point structure of the Higgs-Yukawa model, with its scalar being nonminimally coupled to the asymptotically safe gravity, using the functional renormalization group. We have obtained the renormalization group equations for the cosmological and Newton constants, the scalar mass-squared and quartic coupling constant, and the Yukawa and non-minimal coupling constants, taking into account all the scalar, fermion, and graviton loops. We find that switching on the fermionic quantum fluctuations makes the non-minimal coupling constant irrelevant around the Gaussian-matter fixed point with the asymptotically safe gravity. * Usually, "critical surface" refers to what is called the "IR critical surface" here. In the literature on the asymptotic safety, the wording "UV critical surface" is used frequently, and we put "IR" on what is usually called "critical surface", in order to distinguish it from the other. 10 A background φ = 0 breaks this Z2 symmetry. In this paper, we restrict our attention to the case φ = 0. 11 The ghost Cµ and anti-ghostCµ are treated as fluctuations only.

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“…where Γ[n] is the Gamma function. Thanks to above relations (126) and (128), the trace for the eigenvalues of the derivative operator can be evaluated in curved space.…”

Section: Heat Kernel Tracementioning

confidence: 99%

Non-minimal coupling in Higgs–Yukawa model with asymptotically safe gravity

Oda

Yamada

2016

Class. Quantum Grav.

124

127

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“…One tries to discriminate between a first-and second-(or higher-)order transition by looking at the Binder parameter [191,192,7], or scaling exponents α governing the scaling behaviour ∼ |κ c 2 − κ 2 | α of suitable observables [1,192], or the peak height of susceptibilities as a function of the volume N 4 [16,75,76,14,48,87]. Other scaling relations are discussed in [90,91,96,95]. However, since critical parameters are hard to measure, and it is difficult to estimate finite-size effects, none of the data can claim to be conclusive.…”

Section: Evidence For a Second-order Transition?mentioning

confidence: 99%

Discrete Approaches to Quantum Gravity in Four Dimensions

Loll

1998

Living Rev. Relativ.

176

175

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The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation; quantum Regge calculus; and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.

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“…Our numerical results of the minbu volume distribution in three and four dimensions show a tendency which is also similar to twodimensional case. If we assume that the partition function in three and four dimensions can be written in the same asymptotic form as the two-dimensional case, we obtain the string susceptibility exponents: γ st = −0.05 (6) with N 3 = 16K and γ st = 0.26 (5) with N 4 = 64K near to the critical point.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…In three and four dimensions we have a similar scaling behaviour of the minbu volume. From these scaling date which are shown in Figs.4, 5, we can extract the string susceptibility exponents: γ st = −0.05 (6) with N 3 = 16K and γ st = 0.26 (5) with N 4 = 64K [16].…”

Section: Fractal Structures Of Three-and Four-dimensional Dt Mfdsmentioning

confidence: 99%

“…In the dynamical-triangulation method, calculations of the partition function are performed by replacing the path integral over the metric to a sum over possible triangulations. Over the past few years a considerable number of numerical studies have been made on three-and four-dimensional simplicial quantum gravity [4], and recent results obtained by dynamical triangulation in three and four dimensions suggest the existences of scaling behaviors near to the critical point [5,6] in terms of the geodesic distance [7]. When the coupling strength (κ) becomes close to the critical point from the strong-coupling side (κ < κ c ), which corresponds to the crumple phase, the transition is smooth.…”

Section: Introductionmentioning

confidence: 99%

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Common structures in simplicial quantum gravity

1999

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The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were measured numerically. For spherical boundary surfaces, we obtained a result consistent with the case of a two-dimensional spherical DT surface described by the matrix model. This gives a correct method to reconstruct two-dimensional random surfaces from three-dimensional DT mfds. Furthermore, a scaling property of the volume distribution of minimum neck baby universes was investigated numerically in the case of three and four dimensions, and we obtain a common scaling structure near to the critical points belonging to the strong coupling phase in both dimensions. We have evidence for the existence of a common fractal structure in threeand four-dimensional simplicial quantum gravity. †

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Scaling structures in four-dimensional simplicial gravity

Cited by 6 publications

References 6 publications

Non-minimal coupling in Higgs–Yukawa model with asymptotically safe gravity

Non-minimal coupling in Higgs–Yukawa model with asymptotically safe gravity

Discrete Approaches to Quantum Gravity in Four Dimensions

Common structures in simplicial quantum gravity

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