The Search for the Universality Class of Metric Quantum Gravity

Martini, Riccardo; Ugolotti, Alessandro; Zanusso, Omar

doi:10.3390/universe7060162

Cited by 11 publications

(5 citation statements)

References 88 publications

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“…The use of a vertex-expansion scheme of the effective average action has been also a fertile avenue for the exploration of different truncation schemes of the effective average action in quantum gravity, see [69][70][71][72][73][74][75][76][77]. See also [78][79][80][81][82][83][84][85][86] for discussions of the reconstruction of the bare action from the effective average action in quantum gravity, the running of composite geometric operators, the consequences of background independece to the running of the cosmological constant, and different RG schemes for the search of the UV fixed point. 1 Whether such a fixed point exists beyond finite-dimensional truncations and persists in a Lorentzian setting remains an open challenging problem [119,120], even though the first steps taken in [121][122][123][124] and [57,58,60,125,126] have yielded encouraging results in these directions already.…”

Section: Introductionmentioning

confidence: 99%

Scalar-tensor theories within Asymptotic Safety

Laporte

Pereira

Saueressig

et al. 2021

J. High Energ. Phys.

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Asymptotic Safety provides an elegant mechanism for obtaining a consistent high-energy completion of gravity and gravity-matter systems. Following the initial idea by Steven Weinberg, the construction builds on an interacting fixed point of the theories renormalization group (RG) flow. In this work we use the Wetterich equation for the effective average action to investigate the RG flow of gravity supplemented by a real scalar field. We give a non-perturbative proof that the subspace of interactions respecting the global shift-symmetry of the scalar kinetic term is closed under RG transformations. Subsequently, we compute the beta functions in an approximation comprising the Einstein-Hilbert action supplemented by the shift-symmetric quartic scalar self-interaction and the two lowest order shift-symmetric interactions coupling scalar-bilinears to the spacetime curvature. The computation utilizes the background field method with an arbitrary background, demonstrating that the results are manifestly background independent. Our beta functions exhibit an interacting fixed point suitable for Asymptotic Safety, where all matter interactions are non-vanishing. The presence of this fixed point is rooted in the interplay of the matter couplings which our work tracks for the first time. The relation of our findings with previous results in the literature is discussed in detail and we conclude with a brief outlook on potential phenomenological applications.

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Section: Introductionmentioning

confidence: 99%

Scalar-tensor theories within Asymptotic Safety

Laporte

Pereira

Saueressig

et al. 2021

J. High Energ. Phys.

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show abstract

“…The presence of the new tensor structures on the right-hand sides of equations ( 49) and (50) does not alter the result, since both (M 1 S) and (M 2 A) are traceless. The previous equations are again telling us that the zero modes of ∆ 2,3 are also zero-modes of the tracefree Curtright forms equations ( 49) and (50). Using the same manipulations, we also see that the zero-modes of A µν and S µν are globally orthogonal to their sources, as in the transverse case.…”

Section: Transverse-traceless Decompositionmentioning

confidence: 97%

“…However, from our decomposition it looks like κ ⊥ propagates one negative degree of freedom compensated by one (positive) mode of ζ ⊥ . Even though such an effect is clearly an artifact of an analytic continuation pushed beyond its validity, it would be interesting to inspect whether the limit d → 2 of some dynamical theory of the torsion would exhibit a spectrum with a ghostlike mode for κ ⊥ and one mode for ζ ⊥ , and what would this imply for the corresponding quantum theory 3 .3 Such an approach would resemble what is sometimes done in two-dimensional quantum gravity, where a similar discontinuity of the degrees of freedom happens for the metric[48][49][50][51].…”

mentioning

confidence: 99%

Covariant spin-parity decomposition of the torsion and path integrals

Martini,

Paci,

Sauro

2023

Class. Quantum Grav.

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We propose a functional measure over the torsion tensor. We discuss two completely equivalent choices for the Wheeler-DeWitt supermetric for this field, the first one is based on its algebraic decomposition and the other is inspired by teleparallel theories of gravity. The measure is formally defined by requiring the normalization of the Gaussian integral. To achieve such a result we split the torsion tensor into its spin-parity eigenstates by constructing a new, York-like, decomposition. Of course, such a decomposition has a wider range of applicability to any kind of tensor sharing the symmetries of the torsion. As a result of this procedure a functional Jacobian naturally arises, whose formal expression is given exactly in the phenomenologically interesting limit of maximally symmetric spaces. We also discuss the explicit computation of this Jacobian in the case of a $4$-dimensional sphere $S^4$ with particular emphasis on its logarithmic divergences.

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“…Functional RG methods and a classification of universality classes [18] are not limited to the metric as the quantum degree of freedom. In fact, pioneering studies have been performed for Einstein-Cartan theory with the Hilbert-Palatini action being generalized to the Holst action [19][20][21] or constrained to self-dual connections [22], or for "tetrad only" formulations [23].…”

Section: Introductionmentioning

confidence: 99%

Asymptotically safe Hilbert–Palatini gravity in an on-shell reduction scheme

Gies

Salek

2023

Eur. Phys. J. C

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We study the renormalization flow of Hilbert–Palatini gravity to lowest non-trivial order. We find evidence for an asymptotically safe high-energy completion based on the existence of an ultraviolet fixed point similar to the Reuter fixed point of quantum Einstein gravity. In order to manage the quantization of the large number of independent degrees of freedom in terms of the metric as well as the connection, we use an on-shell reduction scheme: for this, we quantize all degrees of freedom beyond Einstein gravity at a given order that remain after using the equations of motion at the preceding order. In this way, we can straightforwardly keep track of the differences emerging from quantizing Hilbert–Palatini gravity in comparison with Einstein gravity. To lowest non-trivial order, the difference is parametrized by fluctuations of an additional abelian gauge field. The critical properties of the ultraviolet fixed point of Hilbert–Palatini gravity are similar to those of the Reuter fixed point, occurring at a smaller Newton coupling and exhibiting more stable higher order exponents.

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The Search for the Universality Class of Metric Quantum Gravity

Cited by 11 publications

References 88 publications

Scalar-tensor theories within Asymptotic Safety

Scalar-tensor theories within Asymptotic Safety

Covariant spin-parity decomposition of the torsion and path integrals

Asymptotically safe Hilbert–Palatini gravity in an on-shell reduction scheme

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