A proper-time cure for the conformal sickness in quantum gravity

Dasgupta, Arundhati; Loll, R.

doi:10.1016/s0550-3213(01)00227-9

Cited by 91 publications

(148 citation statements)

References 38 publications

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“…This is clearly a non-perturbative effect which involves not just the action, but also the "measure" of the path integral. A similar argument of a non-perturbative cancellation between certain Faddeev-Popov determinants and the conformal divergence can be made in a gauge-fixed continuum computation [20]. 15 This result is reassuring, because it shows that (Euclideanized) path integrals are not doomed to fail, if only they are set up properly and non-perturbatively.…”

Section: In Three Dimensionsmentioning

confidence: 60%

“…Currently this is a somewhat academic question, since it is in practice difficult to find such alternatives. In fact, it is quite miraculous we have found a single prescription for Wick-rotating in our regularized setting, and it does not seem to have a direct continuum analogue (for more comments on this issue, see [20,21]). …”

Section: Lorentzian Nature Of the Path Integralmentioning

confidence: 88%

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A Discrete History of the Lorentzian Path Integral

Loll

2003

Quantum Gravity

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In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach solves the problems of (i) having a welldefined Wick rotation, (ii) possessing a coordinate-invariant cutoff, and (iii) leading to convergent sums over geometries. Although little is known as yet about the existence and nature of an underlying continuum theory of quantum gravity in four dimensions, there are already a number of beautiful results in d = 2 and d = 3 where continuum limits have been found. They include an explicit example of the inequivalence of the Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the cancellation of the conformal factor, and the discovery that causality can act as an effective regulator of quantum geometry.

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Section: In Three Dimensionsmentioning

confidence: 60%

Section: Lorentzian Nature Of the Path Integralmentioning

confidence: 88%

A Discrete History of the Lorentzian Path Integral

Loll

2003

Quantum Gravity

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“…, where C 4 is the same quantity that appeared in (29). For the range of four-volumes used in the simulations, N 4 ∈ [45.000, 360.000], the linear size πR of the quantum de Sitter universes lies between 12 and 21 Planck lengths ℓ P .…”

Section: The Effective Actionmentioning

confidence: 99%

“…Now that we have a UV cut-off, the lattice link length a, we can instead form the dimensionless quantitŷ G = G/a 2 . From (29) it can essentially be identified with the inverse of k 1 , which we can measure. We can reformulate the renormalization group in terms of the new short-distance cut-off as…”

Section: Making Contact With Asymptotic Safetymentioning

confidence: 99%

Quantum Gravity via Causal Dynamical Triangulations

Ambjørn¹,

Görlich²,

Jurkiewicz³

et al. 2014

Springer Handbook of Spacetime

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Abstract"Causal Dynamical Triangulations" (CDT) represent a lattice regularization of the sum over spacetime histories, providing us with a non-perturbative formulation of quantum gravity. The ultraviolet fixed points of the lattice theory can be used to define a continuum quantum field theory, potentially making contact with quantum gravity defined via asymptotic safety. We describe the formalism of CDT, its phase diagram, and the quantum geometries emerging from it. We also argue that the formalism should be able to describe a more general class of quantum-gravitational models of Hořava-Lifshitz type.

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“…It is related to the fact that the Euclidean action for Einstein gravity is not bounded from below, and this is known as the conformal factor problem in Euclidean quantum gravity [49]. It was argued in [50] that the conformal divergence due to the unboundedness of the action might get cancelled with a similar term of opposite sign caused by the measure of the path integral. However, the difference between the action of the solution and that of the background remains positive-valued.…”

Section: Solutions Without Oscillationmentioning

confidence: 99%

Fubini instantons in curved space

Lee

Oh³

et al. 2013

J. High Energ. Phys.

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We study Fubini instantons of a self-gravitating scalar field. The Fubini instanton describes the decay of a vacuum state under tunneling instead of rolling in the presence of a tachyonic potential. The tunneling occurs from the maximum of the potential, which is a vacuum state, to any arbitrary state, belonging to the tunneling without any barrier. We consider two different types of the tachyonic potential. One has only a quartic term. The other has both the quartic and quadratic terms. We show that, there exist several kinds of new O(4)-symmetric Fubini instanton solution, which are possible only if gravity is taken into account. One type of them has the structure with Z 2 symmetry. This type of the solution is possible only in the de Sitter background. We discuss on the interpretation of the solutions with Z 2 symmetry.

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A proper-time cure for the conformal sickness in quantum gravity

Cited by 91 publications

References 38 publications

A Discrete History of the Lorentzian Path Integral

A Discrete History of the Lorentzian Path Integral

Quantum Gravity via Causal Dynamical Triangulations

Fubini instantons in curved space

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