Gauge-invariant coefficients in perturbative quantum gravity
Abstract Heat kernel methods are useful for studying properties of quantum gravity. We recompute the first three heat kernel coefficients in perturbative quantum gravity with cosmological constant to ascertain which ones are correctly reported in the literature. They correspond to the counterterms n...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-12-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-022-11119-w |
| _version_ | 1797863762555830272 |
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| author | Fiorenzo Bastianelli Roberto Bonezzi Marco Melis |
| author_facet | Fiorenzo Bastianelli Roberto Bonezzi Marco Melis |
| author_sort | Fiorenzo Bastianelli |
| collection | DOAJ |
| description | Abstract Heat kernel methods are useful for studying properties of quantum gravity. We recompute the first three heat kernel coefficients in perturbative quantum gravity with cosmological constant to ascertain which ones are correctly reported in the literature. They correspond to the counterterms needed to renormalize the one-loop effective action in four dimensions. They may be evaluated at arbitrary dimensions D, in which case they identify only a subset of the divergences appearing in the effective action for $$D\ge 6$$ D ≥ 6 . Generically, these coefficients depend on the gauge-fixing choice adopted in quantizing the Einstein–Hilbert action. However, they become gauge-invariant once evaluated on-shell, i.e. using Einstein’s equations with cosmological constant. Thus, we identify these gauge invariant coefficients and use them as a benchmark for testing alternative approaches to perturbative quantum gravity. One of these approaches describes the graviton in first-quantization through the $${{\mathcal {N}}}=4$$ N = 4 spinning particle, characterized by four supersymmetries on the worldline and a set of worldline gauge invariances. This description has been used for computing the gauge-invariant coefficients as well. We verify their correctness at $$D=4$$ D = 4 , but find a mismatch at arbitrary D when comparing with the benchmark fixed previously. We interpret this result as signaling that the path integral quantization of the $${{\mathcal {N}}}=4$$ N = 4 spinning particle should be amended. We perform this task by fixing the correct counterterm that must be used in the worldline path integral quantization of the $${{\mathcal {N}}}=4$$ N = 4 spinning particle to make it consistent in arbitrary dimensions. |
| first_indexed | 2024-04-09T22:40:51Z |
| format | Article |
| id | doaj.art-bbf03c6ff9c44a83b1fee0ab1625bd07 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-09T22:40:51Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-bbf03c6ff9c44a83b1fee0ab1625bd072023-03-22T12:12:05ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522022-12-0182121910.1140/epjc/s10052-022-11119-wGauge-invariant coefficients in perturbative quantum gravityFiorenzo Bastianelli0Roberto Bonezzi1Marco Melis2Dipartimento di Fisica e Astronomia “Augusto Righi”, Università di BolognaInstitute for Physics, Humboldt University BerlinDipartimento di Fisica e Astronomia “Augusto Righi”, Università di BolognaAbstract Heat kernel methods are useful for studying properties of quantum gravity. We recompute the first three heat kernel coefficients in perturbative quantum gravity with cosmological constant to ascertain which ones are correctly reported in the literature. They correspond to the counterterms needed to renormalize the one-loop effective action in four dimensions. They may be evaluated at arbitrary dimensions D, in which case they identify only a subset of the divergences appearing in the effective action for $$D\ge 6$$ D ≥ 6 . Generically, these coefficients depend on the gauge-fixing choice adopted in quantizing the Einstein–Hilbert action. However, they become gauge-invariant once evaluated on-shell, i.e. using Einstein’s equations with cosmological constant. Thus, we identify these gauge invariant coefficients and use them as a benchmark for testing alternative approaches to perturbative quantum gravity. One of these approaches describes the graviton in first-quantization through the $${{\mathcal {N}}}=4$$ N = 4 spinning particle, characterized by four supersymmetries on the worldline and a set of worldline gauge invariances. This description has been used for computing the gauge-invariant coefficients as well. We verify their correctness at $$D=4$$ D = 4 , but find a mismatch at arbitrary D when comparing with the benchmark fixed previously. We interpret this result as signaling that the path integral quantization of the $${{\mathcal {N}}}=4$$ N = 4 spinning particle should be amended. We perform this task by fixing the correct counterterm that must be used in the worldline path integral quantization of the $${{\mathcal {N}}}=4$$ N = 4 spinning particle to make it consistent in arbitrary dimensions.https://doi.org/10.1140/epjc/s10052-022-11119-w |
| spellingShingle | Fiorenzo Bastianelli Roberto Bonezzi Marco Melis Gauge-invariant coefficients in perturbative quantum gravity European Physical Journal C: Particles and Fields |
| title | Gauge-invariant coefficients in perturbative quantum gravity |
| title_full | Gauge-invariant coefficients in perturbative quantum gravity |
| title_fullStr | Gauge-invariant coefficients in perturbative quantum gravity |
| title_full_unstemmed | Gauge-invariant coefficients in perturbative quantum gravity |
| title_short | Gauge-invariant coefficients in perturbative quantum gravity |
| title_sort | gauge invariant coefficients in perturbative quantum gravity |
| url | https://doi.org/10.1140/epjc/s10052-022-11119-w |
| work_keys_str_mv | AT fiorenzobastianelli gaugeinvariantcoefficientsinperturbativequantumgravity AT robertobonezzi gaugeinvariantcoefficientsinperturbativequantumgravity AT marcomelis gaugeinvariantcoefficientsinperturbativequantumgravity |