Gauge invariance of the background average effective action

Лавров, П. М.; Reis, Eduardo Antonio dos; Netto, Tibério de Paula; Shapiro, Ilya L.

doi:10.1140/epjc/s10052-019-7153-1

Cited by 10 publications

(4 citation statements)

References 33 publications

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“…This task can be then at best viewed as an incorrectly set exercise and this will not have any impact on physics at all. One of the way to solve this issue with explicit gauge dependence is to use some special formalism like presented in [49][50][51]. This is why in this paper we will not comment any more on the Reuter type of FPs, which were the original basis for the AS program in QG research [40].…”

Section: As For Dimensionless Couplings and Dimensional Transmutation...mentioning

confidence: 99%

Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories

Rachwał

2022

Universe

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We present and discuss well known conditions for ultraviolet finiteness and asymptotic safety. The requirements for complete absence of ultraviolet divergences in quantum field theories and existence of a non-trivial fixed point for renormalization group flow in the ultraviolet regime are compared based on the example of a six-derivative quantum gravitational theory in d=4 spacetime dimensions. In this model, it is possible for the first time to have fully UV-finite quantum theory without adding matter or special symmetry, but by inclusion of additional terms cubic in curvatures. We comment on similarities and some apparent differences between the two approaches, but we show that they are both compatible to each other. Finally, we motivate the claim that actually asymptotic safety needs UV-finite models for providing explicit form of the ultraviolet limit of Wilsonian effective actions describing special situations at fixed points.

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Section: As For Dimensionless Couplings and Dimensional Transmutation...mentioning

confidence: 99%

Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories

Rachwał

2022

Universe

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“…In turn the gauge dependence problem exists for the FRG approach as unsolved ones if one does not take into account the reformulation based on composite operators [41] where the problem was discussed from point of view the basic principles of the quantum field theory. Later on the gauge dependence problem in the FRG was discussed several times for Yang-Mills and quantum gravity theories [42,43,44,45] but the reaction from the FRG community was very weak and came down only to mention without any serious study [46,47,48,49,50]. Situation with the gauge dependence in the FRG is very serious because without solving the problem a physical interpretation of results obtained is impossibly.…”

Section: Introductionmentioning

confidence: 99%

BRST, Ward identities, gauge dependence, and a functional renormalization group

Lavrov

2020

Preprint

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Basic properties of gauge theories in the framework of Faddeev-Popov (FP) method, Batalin-Vilkovisky (BV) formalism, functional renormalization group approach are considered. The FP-and BV-quantizations are characterized by the BRST symmetry while the BRST symmetry is broken in the FRG approach. It is shown that the FP-method, the BV-formalism and the FRG approach can be provided with the Slavnov-Taylor identity, the Ward identity and the modified Slavnov-Taylor identity respectively. It is proved that using the background field method, the background gauge invariance of effective action within the FP and FRG quantization procedures can be achieved in non-linear gauges. The gauge dependence problem within the FP-, BV-and FRG quantizations is studied. Arguments allowing to state impossibility of gauge independence of physical results obtained within the FRG approach are given.

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“…This problem is the subject of the present work. In the previous publications [15,16,17] we explored the gauge fixing dependence in Yang-Mills theories and it was shown that such dependence for the effective average action does not vanish on-shell, except in the fixed point where this object becomes identical with the usual effective action in quantum field theory. Except this special point there is uncontrollable dependence on the set of arbitrary gauge fixing parameters, and thus one can expect a strong arbitrariness in the renormalization group flows which lead to the fixed point and, in fact, define its position and proper existence.…”

Section: Introductionmentioning

confidence: 99%

Functional renormalization group approach and gauge dependence in gravity theories

et al. 2020

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We investigate the gauge symmetry and gauge fixing dependence properties of the effective average action for quantum gravity models of general form. Using the background field formalism and the standard BRST-based arguments, one can establish the special class of regulator functions that preserves the background field symmetry of the effective average action. Unfortunately, regardless the gauge symmetry is preserved at the quantum level, the non-invariance of the regulator action under the global BRST transformations leads to the gauge fixing dependence even under the use of the on-shell conditions.

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Gauge invariance of the background average effective action

Cited by 10 publications

References 33 publications

Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories

Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories

BRST, Ward identities, gauge dependence, and a functional renormalization group

Functional renormalization group approach and gauge dependence in gravity theories

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