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Basic properties of an alternative flow equation in gravity theories

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Abstract

Basic properties of alternative flow equation in quantum gravity are studied. It is shown that the alternative flow equation for effective two-particle irreducible effective action is gauge independent and does not depend on IR parameter k on shell.

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Notes

  1. Standard examples are Einstein gravity, \(S_0(g)=\kappa ^{-2}\int \mathrm{d}x \sqrt{-\mathrm{det}g}\;R\), and \(R^2\) gravity, \(S_0(g)=\int \mathrm{d}x \sqrt{-\mathrm{det}g}\;(\lambda _1 R^2+ \lambda _2R^{\mu \nu }R_{\mu \nu }+\kappa ^{-2}R)\).

  2. The gravitational BRST transformations were introduced in [20,21,22]. For more compact presentation of the BRST transformations, we use the notation \(\delta _B\) for \(\delta _\mathrm{BRST}\).

  3. For recent development of the background field method see [34].

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Acknowledgements

The work is supported by the Ministry of Education of the Russian Federation, Project FEWF-2020-0003.

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Authors and Affiliations

  1. Tomsk State Pedagogical University, Kievskaya St. 60, Tomsk, Russia, 634061

    Peter M. Lavrov

  2. National Research Tomsk State University, Lenin Av. 36, Tomsk, Russia, 634050

    Peter M. Lavrov

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Correspondence to Peter M. Lavrov.

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Lavrov, P.M. Basic properties of an alternative flow equation in gravity theories. Eur. Phys. J. Plus 136, 854 (2021). https://doi.org/10.1140/epjp/s13360-021-01731-2

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