Radiative corrections to the R and R 2 invariants from torsion fluctuations on maximally symmetric spaces
Abstract We derive the runnings of the R and R 2 operators that stem from integrating out quantum torsion fluctuations on a maximally symmetric Euclidean background, while treating the metric as a classical field. Our analysis is performed in a manifestly covariant way, exploiting both the recently-...
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SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)138 |
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| author | Riccardo Martini Gregorio Paci Dario Sauro |
| author_facet | Riccardo Martini Gregorio Paci Dario Sauro |
| author_sort | Riccardo Martini |
| collection | DOAJ |
| description | Abstract We derive the runnings of the R and R 2 operators that stem from integrating out quantum torsion fluctuations on a maximally symmetric Euclidean background, while treating the metric as a classical field. Our analysis is performed in a manifestly covariant way, exploiting both the recently-introduced spin-parity decomposition of torsion perturbations and the heat kernel technique. The Lagrangian we start with is the most general one for 1-loop computations on maximally symmetric backgrounds involving kinetic terms and couplings to the scalar curvature that is compatible with a gauge-like symmetry for the torsion. The latter removes the twice-longitudinal vector mode from the spectrum, and it yields operators of maximum rank four. We also examine the conditions required to avoid ghost instabilities and ensure the validity of our assumption to neglect metric quantum fluctuations, demonstrating the compatibility between these two assumptions. Then, we use our findings in the context of Starobinsky’s inflation to calculate the contributions from the torsion tensor to the β-function of the R 2 term. While this result is quantitatively reliable only at the 0-th order in the slow-roll parameters or during the very early stages of inflation — due to the background choice — it qualitatively illustrates how to incorporate quantum effects of torsion in the path integral formalism. |
| format | Article |
| id | doaj-art-6edbd3c7e0be4f7cb71eff06429924a8 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-6edbd3c7e0be4f7cb71eff06429924a82025-01-05T12:07:03ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241214810.1007/JHEP12(2024)138Radiative corrections to the R and R 2 invariants from torsion fluctuations on maximally symmetric spacesRiccardo Martini0Gregorio Paci1Dario Sauro2INFN — Sezione di PisaINFN — Sezione di PisaINFN — Sezione di PisaAbstract We derive the runnings of the R and R 2 operators that stem from integrating out quantum torsion fluctuations on a maximally symmetric Euclidean background, while treating the metric as a classical field. Our analysis is performed in a manifestly covariant way, exploiting both the recently-introduced spin-parity decomposition of torsion perturbations and the heat kernel technique. The Lagrangian we start with is the most general one for 1-loop computations on maximally symmetric backgrounds involving kinetic terms and couplings to the scalar curvature that is compatible with a gauge-like symmetry for the torsion. The latter removes the twice-longitudinal vector mode from the spectrum, and it yields operators of maximum rank four. We also examine the conditions required to avoid ghost instabilities and ensure the validity of our assumption to neglect metric quantum fluctuations, demonstrating the compatibility between these two assumptions. Then, we use our findings in the context of Starobinsky’s inflation to calculate the contributions from the torsion tensor to the β-function of the R 2 term. While this result is quantitatively reliable only at the 0-th order in the slow-roll parameters or during the very early stages of inflation — due to the background choice — it qualitatively illustrates how to incorporate quantum effects of torsion in the path integral formalism.https://doi.org/10.1007/JHEP12(2024)138Renormalization and RegularizationModels of Quantum GravityCosmological models |
| spellingShingle | Riccardo Martini Gregorio Paci Dario Sauro Radiative corrections to the R and R 2 invariants from torsion fluctuations on maximally symmetric spaces Journal of High Energy Physics Renormalization and Regularization Models of Quantum Gravity Cosmological models |
| title | Radiative corrections to the R and R 2 invariants from torsion fluctuations on maximally symmetric spaces |
| title_full | Radiative corrections to the R and R 2 invariants from torsion fluctuations on maximally symmetric spaces |
| title_fullStr | Radiative corrections to the R and R 2 invariants from torsion fluctuations on maximally symmetric spaces |
| title_full_unstemmed | Radiative corrections to the R and R 2 invariants from torsion fluctuations on maximally symmetric spaces |
| title_short | Radiative corrections to the R and R 2 invariants from torsion fluctuations on maximally symmetric spaces |
| title_sort | radiative corrections to the r and r 2 invariants from torsion fluctuations on maximally symmetric spaces |
| topic | Renormalization and Regularization Models of Quantum Gravity Cosmological models |
| url | https://doi.org/10.1007/JHEP12(2024)138 |
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