Addendum: EPRL/FK Asymptotics and the Flatness Problem

Engle, Jonathan Steven; Kaminski, Wojciech; Oliveira, José Ricardo

doi:10.48550/arxiv.2012.14822

Cited by 5 publications

(6 citation statements)

References 11 publications

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“…( 5) and (6). To remove the gauge freedom, We choose g a , a = 1, 6, 11, 16, 21, to be identity and g a , a = 2, 3,8,9,14,15,17,20,22,23, to be upper triangular matrix. In each 4-simplex, we choose a = 1, 6, 11, 16, 21 as the references and use Eq.…”

Section: F Flipping Orientations and Numerical Resultsmentioning

confidence: 99%

“…Nevertheless, it has been argued that an accidental flatness constraint might emerge in the semiclassical regime, so that spinfoam amplitudes would be dominated by only flat Regge geometries, whereas curved geometries were absent [20][21][22][23][24]. The suspicion of lacking curved geometry in the semiclassical regime has lead to the doubt about the semiclassical behavior.…”

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confidence: 99%

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Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity

Han,

Huang,

Liu

et al. 2021

Preprint

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This paper focuses on the semiclassical behavior of the spinfoam quantum gravity in 4 dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries from the large-j Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude. The dominant contribution from the curved geometry to the spinfoam amplitude is proportional to e iI , where I is the Regge action of the geometry plus corrections of higher order in curvature. As a result, the spinfoam amplitude reduces to an integral over Regge geometries weighted by e iI in the semiclassical regime. As a byproduct, our result also provides a mechanism to relax the cosine problem in the spinfoam model. Our results provide important evidence supporting the semiclassical consistency of the spinfoam quantum gravity. * hanm(AT)fau.edu † hzc881126(AT)hotmail.com ‡ hongguang.liu(AT)gravity.fau.de § dqu2017(AT)fau.edu

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Section: F Flipping Orientations and Numerical Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity

Han,

Huang,

Liu

et al. 2021

Preprint

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“…This example suggest that circling branch points, which result from configurations with null triangles or null tetrahedra, leads to a change in the deficit angles by multiples of 2π n, with n ∈ Z, which is consistent with the behaviour of the angle functions, when circling configurations with null edges. There is another remarkable connection to spin foams [31]: there, instead of integrating over length variables one sums over discrete values for the areas. But, using Poisson resummation, one can rewrite the sum into a sum of integrals over now continuous area parameters.…”

Section: Summary and Discussionmentioning

confidence: 99%

Complex actions and causality violations: applications to Lorentzian quantum cosmology

Asante

Dittrich

Padua-Argüelles

2023

Class. Quantum Grav.

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For the construction of the Lorentzian path integral for gravity one faces two main questions: Firstly, what configurations to include, in particular whether to allow Lorentzian metrics that violate causality conditions. And secondly, how to evaluate a highly oscillatory path integral over unbounded domains. Relying on Picard-Lefschetz theory to address the second question for discrete Regge gravity, we will illustrate that it can also answer the first question. To this end we will define the Regge action for complexified variables and study its analytical continuation. Although there have been previously two different versions defined for the Lorentzian Regge action, we will show that the complex action is unique. More precisely, starting from the different definitions for the action one arrives at equivalent analytical extensions. The difference between the two Lorentzian versions is only realized along branch cuts which arise for a certain class of causality violating configurations. As an application we discuss the path integral describing a finite evolution step of the discretized deSitter universe. We will in particular consider an evolution from vanishing to finite scale factor, for which the path integral defines the no-boundary wave function.

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“…This example suggest that circling branch points, which result from configurations with null triangles or null tetrahedra, leads to a change in the deficit angles by multiples of 2πn, with n ∈ Z, which is consistent with the behaviour of the angle functions, when circling configurations with null edges. There is another remarkable connection to spin foams [31]: there, instead of integrating over length variables one sums over discrete values for the areas. But, using Poisson resummation, one can rewrite the sum into a sum of integrals over now continuous area parameters.…”

Section: Summary and Discussionmentioning

confidence: 99%

Complex actions and causality violations: Applications to Lorentzian quantum cosmology

Asante¹,

Dittrich²,

Padua-Argüelles³

2021

Preprint

View full text Add to dashboard Cite

For the construction of the Lorentzian path integral for gravity one faces two main questions: Firstly, what configurations to include, in particular whether to allow Lorentzian metrics that violate causality conditions. And secondly, how to evaluate a highly oscillatory path integral over unbounded domains. Relying on Picard-Lefschetz theory to address the second question for discrete Regge gravity, we will illustrate that it can also answer the first question. To this end we will define the Regge action for complexified variables and study its analytical continuation. Although there have been previously two different versions defined for the Lorentzian Regge action, we will show that the complex action is unique. More precisely, starting from the different definitions for the action one arrives at equivalent analytical extensions. The difference between the two Lorentzian versions is only realized along branch cuts which arise for a certain class of causality violating configurations.As an application we discuss the path integral describing a finite evolution step of the discretized deSitter universe. We will in particular consider an evolution from vanishing to finite scale factor, for which the path integral defines the no-boundary wave function.

show abstract

Addendum: EPRL/FK Asymptotics and the Flatness Problem

Cited by 5 publications

References 11 publications

Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity

Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity

Complex actions and causality violations: applications to Lorentzian quantum cosmology

Complex actions and causality violations: Applications to Lorentzian quantum cosmology

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