Trace anomaly and infrared cutoffs

Morris, Tim R.; Percacci, Roberto

doi:10.1103/physrevd.99.105007

Cited by 18 publications

(14 citation statements)

References 72 publications

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“…(63) The form of (63) makes it clear that an RG transformation is nothing but an active frame transformation which includes a dilatation step where the conjugate inessential coupling is k itself. This is inline with the observations made in [43] that show a direct relation between the flow of EAA and the anomaly due to the breaking of scale invariance.…”

Section: B Dimensionless Covariant Flowsupporting

confidence: 90%

Essential renormalisation group

Baldazzi,

Zinati,

Falls

2021

Preprint

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We propose a novel scheme for the exact renormalisation group motivated by the desire of reducing the complexity of practical computations. The key idea is to specify renormalisation conditions for all inessential couplings, leaving us with the task of computing only the flow of the essential ones. To achieve this aim, we utilise a renormalisation group equation for the effective average action which incorporates general non-linear field reparameterisations. A prominent feature of the scheme is that, apart from the renormalisation of the mass, the propagator evaluated at any constant value of the field maintains its unrenormalised form. Conceptually, the scheme provides a clearer picture of renormalisation itself since the redundant, non-physical content is automatically disregarded in favour of a description based only on quantities that enter expressions for physical observables. To exemplify the scheme's utility, we investigate the Wilson-Fisher fixed point in three dimensions at order two in the derivative expansion. In this case, the scheme removes all order ∂ 2 operators apart from the canonical term. Further simplifications occur at higher orders in the derivative expansion. Although we concentrate on a minimal scheme that reduces the complexity of computations, we propose more general schemes where inessential couplings can be tuned to optimise a given approximation. We further discuss the applicability of the scheme to a broad range of physical theories.

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Section: B Dimensionless Covariant Flowsupporting

confidence: 90%

Essential renormalisation group

Baldazzi,

Zinati,

Falls

2021

Preprint

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“…The goal of this section is to clarify this point. We follow [382], see also [284], section 6.9 12 .…”

Section: Rg Improvementmentioning

confidence: 99%

“…For the effective average action given in Equation 1one finds that the anomaly is given by [382] A ∼ ǫ…”

Section: Rg Improvementmentioning

confidence: 99%

Critical Reflections on Asymptotically Safe Gravity

et al. 2020

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Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, toward answering them. Finally, we also take the opportunity to clarify some common misunderstandings regarding the program.

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“…Scale invariance is in any case broken in the quantum theory because of the running of couplings under the Renormalization Group (RG). However, there may be Fixed Points (FP), where the beta functions vanish and one achieves quantum scale invariance [18,19]. If a RG trajectory reaches a FP in the UV, it describes a UV complete theory.…”

Section: Towards Quantum Magmentioning

confidence: 99%