The origin of Weyl gauging in metric-affine theories

Sauro, Dario; Zanusso, Omar

doi:10.1088/1361-6382/ac82a2

Cited by 13 publications

(9 citation statements)

References 57 publications

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“…This field contributes, for instance, to the trace of the Cartan torsion, T α μα = 3A μ [40,41]. For the discussion of a relation to the affine Weyl connection, see [42,43].…”

Section: Einstein-hilbert-palatini Actionmentioning

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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“…This field contributes, for instance, to the trace of the Cartan torsion, T α μα = 3A μ [40,41]. For the discussion of a relation to the affine Weyl connection, see [42,43].…”

Section: Einstein-hilbert-palatini Actionmentioning

confidence: 99%

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

Gies

Salek

2023

Eur. Phys. J. C

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“…The suggestion, pushed forward in Refs. [16,17], is to constrain the degrees of freedom of a general MAG using symmetry requirements, and in particular Weyl and conformal invariance. In particular, while the vectors in the expansions of both torsion and nonmetricity can be used to construct models with gauged Weyl symmetry, the hooksymmetric and antisymmetric tensors can enjoy fully conformal invariant actions without the need of gauging the covariant derivative, provided that κ and ψ are dimensionless fields.…”

Section: A General Tensor Decompositions Of Torsion and Nonmetricitymentioning

confidence: 99%

“…The coupling w v is the Weyl weight of v µ and is the charge of the gauged Weyl transformation. The covariant derivative ∇ is not the direct sum of the Levi-Civita and a gauge one because dilatations do not commute with the local Lorentz group, still the semidirect product of the generated group is a subgroup of GL(d) [17].…”

Section: Appendix A: Algebraic Reduction Of the Independent Termsmentioning

confidence: 99%

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Conformally covariant operators of mixed-symmetry tensors and MAGs

Paci¹,

Sauro²,

Zanusso³

2023

Preprint

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We compute conformally covariant actions and operators for tensors with mixed symmetries in arbitrary dimension d. Our results complete the classification of conformal actions that are quadratic on arbitrary tensors with three indices, which allows to write corresponding conformal actions for all tensor species that appear in the decomposition of the distorsion tensor of an arbitrary metricaffine theory of gravity including both torsion and nonmetricity. We also discuss the degrees of freedom that such theories are propagating, as well as interacting metric-affine theories that enjoy the conformal actions in the Gaussian limit.

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“…. The suggestion, pushed forward in [23,24], is to constrain the degrees of freedom of a general MAG using symmetry requirements, and in particular Weyl and conformal invariance. In particular, while the vectors in the expansions of both torsion and nonmetricity can be used to construct models with gauged Weyl symmetry, the hook-symmetric and antisymmetric tensors can enjoy fully conformal invariant actions without the need of gauging the covariant derivative, provided that κ and ψ are dimensionless fields.…”

Section: General Tensor Decompositions Of Torsion and Nonmetricitymentioning

confidence: 99%

Conformally covariant operators of mixed-symmetry tensors and MAGs

Paci,

Sauro,

Zanusso

2023

Class. Quantum Grav.

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We compute conformally covariant actions and operators for tensors with mixed symmetries in arbitrary dimension d. Our results complete the classiﬁcation of conformal actions that are quadratic on arbitrary tensors with three indices, which allows to write corresponding conformal actions for all tensor species that appear in the decomposition of the distorsion tensor of an arbitrary metric-aﬃne theory of gravity including both torsion and nonmetricity. We also discuss the degrees of freedom that such theories are propagating, as well as interacting metric-aﬃne theories that enjoy the conformal actions in the Gaussian limit.

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The origin of Weyl gauging in metric-affine theories

Cited by 13 publications

References 57 publications

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

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

Conformally covariant operators of mixed-symmetry tensors and MAGs

Conformally covariant operators of mixed-symmetry tensors and MAGs

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