Affine-metric quantum gravity with extra local symmetries

Kalmykov, M.Yu.

doi:10.1088/0264-9381/14/2/010

Cited by 6 publications

(6 citation statements)

References 69 publications

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“…Secondly, the particles of the standard models are also known to inhibit projective symmetry. Some properties of the projective invariance at quantum level are discussed in [30][31][32][33].…”

Section: )mentioning

confidence: 99%

Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?

Aoki

Shimada

2019

Phys. Rev. D

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We reveal the existence of a certain hidden symmetry in general ghost-free scalar-tensor theories which can only be seen when generalizing the geometry of the spacetime from Riemannian. For this purpose, we study scalar-tensor theories in the metric-affine (Palatini) formalism of gravity, which we call scalar-metric-affine theories for short, where the metric and the connection are independent. We show that the projective symmetry, a local symmetry under a shift of the connection, can provide a ghost-free structure of scalar-metric-affine theories. The ghostly sector of the secondorder derivative of the scalar is absorbed into the projective gauge mode when the unitary gauge can be imposed. Incidentally, the connection does not have the kinetic term in these theories and then it is just an auxiliary field. We can thus (at least in principle) integrate the connection out and obtain a form of scalar-tensor theories in the Riemannian geometry. The projective symmetry then hides in the ghost-free scalar-tensor theories. As an explicit example, we show the relationship between the quadratic order scalar-metric-affine theory and the quadratic U-degenerate theory. The explicit correspondence between the metric-affine (Palatini) formalism and the metric one could be also useful for analyzing phenomenology such as inflation.1 In the paper [16], U-degenerate theories and DHOST theories are classified: U-degenerate theories are not degenerate in an arbitrary gauge but degenerate in the unitary gauge while DHOST theories are degenerate under any gauge. However, in the present paper, we will just call theories "U-degenerate theories" if the Lagrangian is degenerate at least in the unitary gauge for simplicity.

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Section: )mentioning

confidence: 99%

Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?

Aoki

Shimada

2019

Phys. Rev. D

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“…An immediate use of the expression (43) is that it can be rearranged to give an important expression for the A gauge field. Defining the quantities…”

Section: E Alternative Form Of Covariant Derivative In Wgtmentioning

confidence: 99%

“…The lack of a clear route to quantising PGT has led to interest in imposing extra gauge symmetries beyond local Poincaré symmetry, since this could, in principle, lead to surprises that might allow for a simultaneously unitary and renormalizable theory 31,43 , without having to resort to non-local theories [44][45][46] . In particular, perhaps the most natural extension of PGT is also to demand local scale invariance, which might resolve some of the problems outlined above 47 , since such theories contain no absolute energy scale.…”

Section: Introductionmentioning

confidence: 99%

Scale-invariant gauge theories of gravity: Theoretical foundations

Lasenby

Hobson²

2016

Journal of Mathematical Physics

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We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincaré invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations, which allow for a more transparent interpretation of such theories in terms of gauge fields in Minkowski spacetime. Our approach therefore differs from the usual geometrical description of locally scale-invariant Poincaré gauge theory (PGT) and Weyl gauge theory (WGT) in terms of Riemann-Cartan and Weyl-Cartan spacetimes, respectively. In particular, we reconsider the interpretation of the Einstein gauge and also the equations of motion of matter fields and test particles in these theories. Inspired by the observation that the PGT and WGT matter actions for the Dirac field and electromagnetic field have more general invariance properties than those imposed by construction, we go on to present a novel alternative to WGT by considering an 'extended' form for the transformation law of the rotational gauge field under local dilations, which includes its 'normal' transformation law in WGT as a special case. The resulting 'extended' Weyl gauge theory (eWGT) has a number of interesting features that we describe in detail. In particular, we present a new scale-invariant gauge theory of gravity that accommodates ordinary matter and is defined by the most general parity-invariant eWGT Lagrangian that is at most quadratic in the eWGT field strengths, and we derive its field equations. We also consider the construction of PGTs that are invariant under local dilations assuming either the 'normal' or 'extended' transformation law for the rotational gauge field, but show that they are special cases of WGT and eWGT, respectively.

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“…where the couplings X 1 , X 2 and X 3 are fixed based on the symmetry property of A ρ µ ν and ξ µ (x) is the local parameter. The consequences of the invariance under (3.1) have been widely investigated [21,[41][42][43][44]. We highlight, in particular, how their role to guarantee a theory free of Ostrogradsky ghosts was analyzed in [36] for the more limited case of linear curvature theories.…”

Section: Use Of Symmetries In Magmentioning

confidence: 99%

Radiatively stable ghost and tachyon freedom in Metric Affine Gravity

Marzo

2021

Preprint

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We report the existence of a ghost-and tachyon-free sector in metric-affine theories of gravity, that is invariant under diffeomorphism and a particular abelian symmetry. In contrast with many studied cases in the literature, the constraints for unitarity and causality are granted by non-accidental symmetries and do not ask for further tuning, whose fate under renormalization would be unclear. Unsurprisingly, the minimal model is massless. We find that a mechanism to provide mass is accommodated by a simple Stueckelberg extension of metric-affine gravity involving the non-metricity tensor. A non-trivial result is that also such an extension describes a ghost-and tachyon-free dynamic stabilized by the same abelian symmetry. The resulting spectrum of the collective rank-3, rank-2, and rank-0 Lagrangian is investigated with the operators recently computed in the literature.

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Affine-metric quantum gravity with extra local symmetries

Cited by 6 publications

References 69 publications

Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?

Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?

Scale-invariant gauge theories of gravity: Theoretical foundations

Radiatively stable ghost and tachyon freedom in Metric Affine Gravity

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